Lenvatinib Plus Pembrolizumab in Well Differentiated G3 Neuroendocrine Tumors

Inclusion Criteria: 1. Participants must have locally advanced or unresectable histologically or cytologically confirmed WD G3 NET. 1. pancreas primary. 2. other primary sites: * gastrointestinal site, * unknown primary site, * lung neuroendocrine carcinoma with carcinoid morphology, or * other non-pancreatic primary sites with well-differentiated (WD) morphology and Ki67 \> 20%. 3. WD G3 NET occurring de novo or in the setting of grade progression allowed (provided WD G3 NET is thought to be the dominant histology at the time of enrollment). 4. Tumors with ambiguous histology and/or Ki67 \>/=55% must be reviewed at the participating site to confirm that they are not poorly differentiated. Tumors with confirmed ambiguous histology will be considered eligible. 2. At least 1 measurable target lesion according to RECIST 1.1, including the following criteria. 1. non-nodal lesion that measures \>=1.0 cm in the longest diameter. 2. lymph node (LN) lesion that measures as \>=1.5 cm in the short axis. 3. the lesion is suitable for repeat measurement using computed tomography (CT) / magnetic resonance imaging (MRI) (CT/MRI). 4. lesions previously treated with radiation or other locoregional therapy are considered measurable if progression has been demonstrated in such lesions. 5. in the setting of grade progression, every attempt should be made to select measurable target lesions that are thought to represent G3 disease (based on biopsy results, tumor growth rate, or other features). 3. Eligibility for HP 13C MR (applicable only to UCSF patients who meet the requirements below)- up to 10 patients (if machine is functional, available and scheduling allows): 1. At least 1 lesion that is deemed suitable for imaging by HP 13C MR by the investigators (ideally separate from the biopsy site, if planned). 2. No contraindications to MRI. 3. No prior local therapy to the target lesions (s) -unless clear progression in the lesions(s). 4. NOTE: University of California, San Francisco (UCSF) patients who do not meet this requirement will still be allowed to participate if they otherwise meet all eligibility requirements (this criterion should be recorded as "NA" on the eligibility checklist). In other words, the inability to complete HP 13C MR imaging will not preclude study participation) 4. Radiographic evidence of progressive disease within 6 months. a. Required unless 1L in the setting of clinically significant tumor burden and/or tumor with unfavorable biology (e.g. Ki67 \>/=55%, rapid growth rate, fluorodeoxyglucose (FDG)-avid tumor, and/or negative Somatostatin receptor (SSTR)-based Positron Emission Tomography (PET) imaging) 5. Age \>=18 years. a. Because no dosing or adverse event data are currently available on the use of lenvatinib plus pembrolizumab in patients \<18 years of age, children are excluded from this study but will be eligible for future pediatric trials. 6. Eastern Cooperative Oncology Group (ECOG) performance status \<= 1. 7. Have adequate organ function as defined below (Specimens must be collected within 14 days prior to the start of study treatment): * Adequate bone marrow function: * Absolute neutrophil count \>=1,500/microliter (mcL) * Platelets \>=100,000/mcL * Hemoglobin \>=1,500/mcL * Hemoglobin \>=9.0 g/dL or \>=5.6 mmol/L. * Adequate hepatic function, * Total bilirubin \<=1.5 X institutional upper limit of normal, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits. * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) (serum glutamic-pyruvic transaminase (SGPT) \<=2.5 X institutional upper limit of normal (ULN) (\<=5 × ULN for participants with liver metastases). * Adequate renal function, * Creatinine \<= 1.5 x institutional upper limit of normal OR * Creatinine clearance \>=30 mL/min for participant with creatinine levels \>1.5 × institutional ULN, * Urine protein-to-creatinine ratio (UPCR) \<1 (unless urine protein \<1 g/24 hour) OR * Urine protein dipstick \<= 1+(unless urine protein \<1 g/24 hour). * Coagulation: International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) \<=1.5 × ULN unless participant is receiving anticoagulant therapy (and PT or aPTT is within therapeutic range of intended use of anticoagulants). 8. Participant (or legally acceptable representative) must have the ability to understand a written informed consent document, and the willingness to sign it. 9. Adequately controlled blood pressure (BP) with or without anti-hypertensive medications, defined as BP \<140/90 (NOTE: BP should be controlled without a change in medications within one week of day 1 cycle 1). 10. Individuals with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial. 11. Must have a life expectancy of greater than 3 months, as determined by the investigator. 12. Stage 2 patients must agree to have a biopsy of the primary tumor or metastatic tissue at baseline, and there must be a lesion that can be biopsied with acceptable clinical risk (as judged by the investigator). 1. Patients with unsuccessful baseline biopsies may undergo an additional biopsy attempt (at the same or a different site, determined by the investigator). 2. If no metastatic site can be safely biopsied, a biopsy of the primary tumor is acceptable, but must be approved by the principal investigator. 3. Baseline tumor biopsy may be omitted if the tumor is inaccessible and/or a biopsy is thought to post high procedural risk due to location or other factors; or ••If participants have only 1 small (\<1.5cm) measurable lesion per RECIST 1.1, and no non-target lesions amenable to biopsy. 4. If fresh tumor tissue cannot be collected, the overall study (lead-site) PI may approve the use of archival tissue. The use of archival tissue in lieu of a fresh tumor biopsy is encouraged and will be evaluated on a case-by-case basis and must be approved by the overall study (lead-site) PI. * Formalin-fixed, paraffin-embedded (FFPE) tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue. 13. Male participants are eligible to participate if they agree to the following starting with the first dose of study therapy through 7 days after the last dose of lenvatinib (and refrain from donating sperm during this period). * Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) and agree to remain abstinent OR Must agree to use contraception (see appendix 5) unless confirmed to be azoospermic (vasectomized or secondary to medical cause) as detailed below: * Agree to use a male condom plus partner use of an additional contraceptive method when having penile-vaginal intercourse with a WOCBP who is not currently pregnant. Note: Men with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penile-vaginal penetration. * Please note that 7 days after lenvatinib is stopped, if the participant is on pembrolizumab only, no male contraception measures are needed. 14. Female participants are eligible if not pregnant or breastfeeding, and at least 1 of the following conditions applies during the intervention period and for at least 120 days post pembrolizumab or 30 days post lenvatinib, whichever occurs last: * Not be a woman of childbearing potential (WOCBP), e.g., postmenopausal (no menses for \> 1 year) or permanently sterilized. * Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency. * Abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long-term and persistent basis) NOTE: The investigator should evaluate the potential for contraceptive method failure (i.e., noncompliance, recently initiated) in relationship to the first dose of study intervention. Exclusion Criteria: 1. Has poorly differentiated neuroendocrine carcinoma (e.g., small cell NEC, large cell NEC, Merkel cell carcinoma, prostate neuroendocrine carcinoma) or WD Grades 1 or 2 NET (without evidence of G3 NET). 2. Uncontrolled blood pressure (BP) (Systolic BP \>=140 mmHg or diastolic BP \>=90 mmHg) despite an optimized regimen of antihypertensive medication. 3. Significant gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib. 4. Has pre-existing \>= grade 3 (G3) gastrointestinal or non-gastrointestinal fistula. 5. Has clinically significant cardiovascular disease within 12 months from the first dose of study intervention, including New York Heart Association (NYHA) Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability. Note: Medically controlled arrhythmia would be permitted 6. Radiographic evidence of major blood vessel invasion/infiltration (e.g., carotid artery) or intratumoral cavitation in the chest (e.g. tumors above the diaphragm). The degree of tumor invasion/infiltration of major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy. NOTE: Vascular encasement may be allowed in selected cases below the diaphragm; clinical judgement must be employed. Eligible tumors may include: 1. Portal vein or inferior vena cava involvement by tumor is allowed at the discretion of the investigator (and is distinguished from invasion through the wall of a vessel. 2. Vascular encasement by tumor below diaphragm is allowed at the discretion of the investigator, Examples of potentially eligible tumors include: mesenteric mass encasing superior mesenteric artery (SMA)/superior mesenteric vein (SMV), splenic vein involvement from a pancreas primary tumor, or lymphadenopathy adjacent to the inferior vena cava, portal vein, or other vessels without a clear plane between the tumor and vessel). * Vascular encasement by the tumor in the abdomen, such as a mesenteric mass encasing the SMV/SMA, must be distinguished from invasion through the wall of a vessel and with consideration of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy. 7. Active hemoptysis or tumor bleeding (bright red blood of at least 0.5 teaspoons) within 3 weeks prior to the first dose of study drug. 8. Hypersensitivity (\>=G3) or known intolerance to lenvatinib or pembrolizumab or any of its excipients. 9. Serious non-healing wound, ulcer, or bone fracture. 10. Bleeding or thrombotic disorders or participants at risk for severe hemorrhage. 11. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. 12. Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. 1. Individuals with new or progressive asymptomatic small (\<1 cm) brain metastases are eligible if the treating physician determines that immediate CNS-specific treatment is not required and is unlikely to be required during the first cycle of therapy. 2. Participants with previously treated brain metastases (e.g., whole brain radiation therapy, surgery, or radiosurgery) may participate provided they are radiologically stable (i.e., without evidence of progression by imaging) for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to the first dose of study intervention. 13. Has an active autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs). a.Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 14. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 15. Has an active infection requiring systemic therapy. 16. Has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by a local health authority. 17. Has a known history of hepatitis B (defined as hepatitis B surface antigen (HBsAg) reactive) or known active hepatitis C virus (HCV) (defined as HCV RNA \[qualitative\] is detected) infection. Note: No testing for hepatitis B (HBV) and hepatitis C is required unless mandated by a local health authority. 1. Participants with controlled hepatitis C are eligible (no detectable HCV RNA qualitative) provided anti-viral therapy completed at least 4 weeks prior to enrollment. 2. Participants with controlled HBV are eligible if they meet the following criteria: * Antiviral therapy for HBV must be given for at least 4 weeks and HBV viral load must be less than 500 IU/mL before the first dose of study drug. Participants on active HBV therapy with viral loads under 100 IU/mL should stay on the same therapy throughout study treatment. * Participants who are positive for anti-Hepatitis B Core (HBc), negative for HbsAg, and negative or positive for anti-HBs, and who have an HBV viral load under 100 IU/mL, do not require HBV antiviral prophylaxis 18. Is known to have active tuberculosis (TB, Bacillus tuberculosis). 19. Diagnostic assessments: 1. Participants with urine protein creatinine ratio (UPCR) \>1 or proteinuria \>-2+ (\>=100 mg/dL) on urinalysis/urine dipstick testing will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein \>=1 g/24 hour will be ineligible. 2. Prolongation of QTc interval to \> 480 milliseconds (ms). Investigator may use the average of 3 triplicates if screening QTc \> 450 ms. Rescreening is allowed after discontinuation of any drugs known to prolong QTc. NOTE: If the QTcF is prolonged to \>480 ms in the presence of a pacemaker, the participant will not be excluded if the participant is considered at low risk for ventricular arrhythmias by the investigator. 3. Left ventricular ejection fraction (LVEF) below the institutional (or local laboratory) normal range as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO). 20. Pregnant women are excluded from this study because lenvatinib plus pembrolizumab are products with the potential for teratogenic or abortifacient effects. * A woman of child bearing potential (WOCBP) must have a negative highly sensitive pregnancy test (urine or serum) within 14 days of the first dose of the study intervention. * If a urine test cannot be confirmed as negative (e.g., a positive or an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. * Similarly, a WOCBP must have a negative urine pregnancy test if the serum pregnancy test is positive (and thought to be spurious/from underlying malignancy). 21. Women who are breastfeeding are excluded from the study because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenvatinib plus pembrolizumab (breastfeeding should be discontinued if the mother is treated with lenvatinib plus pembrolizumab). 22. Has a history or current evidence of any condition, therapy, or laboratory abnormality (including electrolyte abnormalities that have not been corrected, e.g., potassium, calcium, magnesium) that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator. 23. Has known psychiatric or substance abuse disorders that would interfere with cooperating with the requirements of the study. Listed below are specific concomitant therapies or vaccinations that are prohibited during the study (exceptions noted): 24. Currently participating in or has participated in a trial of an investigational device within 4 weeks prior to the first dose of trial treatment. 25. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks or 5 times the half-life time, whichever is shorter prior to study treatment start. Participants must have recovered from all adverse events (AE) due to previous therapies to \<=Grade 1 (except for alopecia) or baseline, and \<=Grade 2 for neuropathy. 1. Concomitant administration of hormone therapy for breast cancer, and luteinizing hormone-releasing hormone (LHRH) analogs for prostate cancer allowed. 2. Concomitant somatostatin analogs for functional neuroendocrine tumors are allowed as per standard of care assuming a stable dose for at least two months and progressive disease has been documented on that dose. 3. Note: Participants who have entered the follow-up phase of an investigational study may participate if it has been 4 weeks after the last dose of the previous investigational agent. 26. Has received prior treatment with lenvatinib, or any anti-programmed cell death protein 1 (PD-1), anti-programmed death-ligand 1 (PD-L1), or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), OX 40, CD137). Treatment with another Vascular Endothelial Growth Factor Inhibitor (VEGF inhibitor\_ (besides lenvatinib) is allowed if at least 6 months have elapsed since discontinued therapy. 27. Has received prior radiotherapy within 2 weeks of the start of study treatment. Participants must have recovered from all radiation-related toxicities (to Grade \<=1), not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (\<=2 weeks of radiotherapy) for non-CNS disease. 28. Has had major surgery within 3 weeks prior to the first dose of study interventions. Note: Adequate wound healing after major surgery must be assessed clinically, independent of time elapsed for eligibility. 29. Has had an allogeneic tissue/solid organ transplant. 30. Patients who are currently receiving medication with a known risk of prolonging the QT interval inducing Torsade's de Pointes (TdP) and the treatment cannot either be discontinued or switched to a different medication prior to starting study drug treatment. A list of prohibited drugs with a known risk of TdP is provided in Appendix 6. 31. Biologic response modifiers (e.g., granulocyte colony-stimulating factor) within 4 weeks before study entry. Chronic erythropoietin therapy is permitted provided that no dose adjustments were made within 2 months before the first dose of study drug. 32. Received a live or attenuated vaccine within 30 days of the planned start of study treatment (C1D1). Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. Coronavirus disease of 2019 (COVID-19) vaccinations are also allowed.