Phase II Study of Pirtobrutinib, Rituximab (PR) in Previously Untreated Low and Intermediate Risk MCL (Mantle Cell Lymphoma) Patients

Inclusion Criteria: The study will enroll 50 previously untreated low and medium risk MCL patients. Estimated 3 patients per month at minimum for enrollment. 1. Age ≥ 18 years old 2. Pathology confirmed diagnosis of mantle cell lymphoma. CD20 positivity is needed. Cyclin D1 negative MCL are allowed after confirming the diagnosis of MCL from hem-path at MDACC. 3. Newly diagnosed MCL with no prior therapy for MCL (age \>= 18 years) • Low risk - Ki-67% (\<= 30%), no features of high-risk disease (see below in exclusion), largest tumor size \<= 3 cm. * Medium risk - Ki-67% (\<=50%), largest tumor size \<=5 cm, no features of high-risk disease (see below in exclusion) 4. Participants with preexisting well-controlled cardio-vascular comorbidities - participants on anticoagulants (excluding warfarin and vitamin K antagonists), antiplatelet, anti-hypertensive, prior ablation, anti-arrhythmia, prior arrhythmias, baseline EKG abnormalities and cardiology clearance are allowed. Ejection fraction \>=50% and cardiology evaluation may be needed. (Echo and EKG and cardiology consultation within 2 months prior to C1D1 are allowed). 5. Understand and voluntarily sign an IRB-approved informed consent form. 6. Participants may have at least 1 site of radiographically assessable disease (i.e., lymph node longest diameter \[LDi\] \>= 1.5 cm, not necessary for disease assessable by positron emission tomography \[PET\]/computerized tomography \[CT\], extra nodal site \>= 1.0 cm in LDi. But participants with isolated gastrointestinal, bone marrow or spleen only disease patients are allowed. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less (See Appendix III). 8. Prothrombin time (or international normalized ratio) and partial thromboplastin time not to exceed 1.2 times the institutional upper limit of normal range (participants with an elevated prothrombin time and known lupus anticoagulant may be eligible for participation after consulting the study PI). 9A. Adequate BM function independent of growth factor or PRBC or platelet transfusion support (within 14 days of Screening assessment and criteria must be met on C1D1 without transfusion/G-CSF within 7 days of assessment, per local laboratory reference range at screening as follows: a. platelet count \>=75,000/mm3; b. absolute neutrophil count (ANC) \>= 1000/mm3 unless cytopenia is clearly due to marrow involvement from MCL c. total hemoglobin \>= 8 g/dL (without transfusion support within 2 weeks of screening); If any of the above-mentioned cytopenias (a-c) are present due to significant BM involvement, at least 30% BM involvement by MCL (requiring transfusion or granulocyte colony-stimulating factor \[G-CSF\] support) MCL patients may proceed with enrollment after discussion with the PI or Co-PI. Cytopenias may not be due to evidence of myelodysplastic syndrome (MDS) or hypoplastic BM. 9B. Adequate organ function as defined by the following laboratory values: a. Creatinine clearance. \>=30 mL/min (by Cockcroft-Gault method, APPENDIX I), b. Total bilirubin ≤ 1.5 × ULN or ≤ 3 × ULN with documented liver involvement and/or Gilbert's Disease or controlled immune hemolysis or considered an effect of regular blood transfusions. c. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<3 x ULN, or \< 5 x upper limit of normal if hepatic metastases are present. 10\. Projected life expectancy of \>12 weeks pertaining to lymphoma. 11. Female participants must be surgically sterile, postmenopausal (for at least 1 year), or have confirmed negative results for a pregnancy test at screening, on a serum sample obtained within 7 days prior to initiation of study treatment. 12\. Women of childbearing potential and men with female partners of childbearing potential must be willing to use a highly effective form of contraception for at least 1 month after the last dose of study treatment. Participant enrolled into the Pirtobrutinib+ rituximab study should use a highly effective form of contraception for 1 month after the last dose of Pirtobrutinib and 12 months after the last dose of rituximab, whichever time period is longer. Recommended methods of highly effective birth control are: 1. Combined estrogen and progestin containing hormonal contraception associated with inhibition of ovulation given orally, intravaginally, or transdermally 2. Progestin-only hormonal contraception associated with inhibition of ovulation given orally, by injection, or by implant 3. Intrauterine device (IUD) 4. Intrauterine hormone-releasing system (IUS) 5. Vasectomized partner 6. Sexual abstinence: considered a highly effective method only if defined as refraining from heterosexual intercourse during an entire period of risk associated with the study treatment. The reliability of sexual abstinence will be evaluated in relation to the duration of the study and to the usual lifestyles of the participant. 7. Female sterilization 8. Fallopian tube implants (if confirmed by hysterosalpingogram) 13. Oocyte donation is prohibited during the duration of participation on this protocol and for 1 month after the last dose of Pirtobrutinib. Exclusion Criteria: 1. Participants with central nervous system involvement with mantle cell lymphoma or with suspected or confirmed progressive multifocal leukoencephalopathy (PML) are excluded since those participants have very poor prognosis, need aggressive intensive chemoimmunotherapy and intrathecal chemotherapy along with BTK inhibitors and these participants would not be eligible for this study. 2. High risk MCL - any or all of the following (Blastoid/pleomorphic histology), High Ki-67 (\>50%), Bulky disease (nodes \>5 cm, spleen \>20 cm), lymphocytosis \>=50,000 cells/uL, TP53 mutated or del17p by FISH. Presence of MYC rearrangement positive by FISH or MYC, Bcl2 amplification, complex karyotype or high-risk biologic MIPI (with Ki-67%) 3. Major surgery within 4 weeks prior to registration 4. History of bleeding diathesis 5. Known active CMV. Unknown or negative status are eligible 6. Evidence of other clinically significant uncontrolled condition(s) including but not limited to, uncontrolled systemic bacterial, viral, fungal or parasitic infection (except for fungal nail infection), or other clinically significant active disease process which in the opinion of the investigator and medical monitor may pose a risk for participant participation. Screening for chronic conditions is not required 7. Clinically significant cardiovascular diseases as determined after cardiology consultation, including uncontrolled or symptomatic arrhythmias, congestive heart failure or myocardial infarction within 6 months of screening or any Class 3 (moderate) or 4 (severe) cardiac disease following the New York Heart Association Classification. Otherwise, significant screening electrocardiogram (ECG) abnormalities including left bundle branch block, 2nd degree AV block type II, 3rd degree block, bradycardia, or QTc \>470 msec. 8. Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction. 9. Pregnancy or plan to become pregnant during the study or within 1-month post pirtobrutinib or 12 months post Rituxan. (Note: post rituxan, WOCBP should not become pregnant for 12 months post last dose of rituxan). 10. Lactation during the study or for 1 week after last dose of pirtobrutinib (Note that the USPI for rituxan recommends no lactation during treatment and for 6 months after last dose) 11. Current treatment with certain strong cytochrome P450 3A4 (CYP3A4) inhibitors or inducers and/or strong P-gp inhibitors. Because of their effect on CYP3A4, use of any of the following within 3 days of study therapy start or planned use during study participation is prohibited - grapefruit or grapefruit products, Seville oranges or products from Seville oranges, star fruit 12. Participants taking warfarin and/or equivalent vitamin K antagonists 13. Has difficulty with or is unable to swallow oral medication or has significant gastrointestinal disease that would limit absorption of oral medication. 14. History of stroke or intracranial hemorrhage within 6 months of C1D1 15. Vaccination with live vaccine within 28 days prior to enrollment. 16. Have a known hypersensitivity to any of the excipients of Pirtobrutinib or rituximab 17. Participants who experienced a major bleeding event or grade ≥ 3 arrhythmia on prior treatment with a BTK inhibitor. NOTE: Major bleeding is defined as bleeding having one or more of the following features: potentially life-threatening bleeding with signs or symptoms of hemodynamic compromise; bleeding associated with a decrease in the hemoglobin level of at least 2g per deciliter; or bleeding in a critical area or organ (e.g., retroperitoneal, intraarticular, pericardial, epidural, or intracranial bleeding or intramuscular bleeding with compartment syndrome). 18. Participants who have tested positive for Human Immunodeficiency Virus (HIV) are excluded due to risk of opportunistic infections with both HIV and BTK-inhibitors. For patients with unknown HIV status, HIV testing will be performed at Screening and result must be negative for enrollment 19. Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection based on criteria below: Hepatitis B virus (HBV): Participants with positive hepatitis B surface antigen (HBsAg) are excluded. Patients with positive hepatitis B core antibody (anti-HBc) and negative HBsAg require hepatitis B polymerase chain reaction (PCR) evaluation before enrollment. Participants who are hepatitis B PCR positive will be excluded unless cleared by infectious disease. If a participant is Hep B core antibody positive, they must be on an approved nucleos(T)ide analogue to help prevent reactivation. Hepatitis C virus (HCV): positive hepatitis C antibody. If positive hepatitis C antibody result, participant will need to have a negative result for hepatitis C ribonucleic acid (RNA) before enrollment, unless cleared by infectious disease. Participants who are hepatitis C RNA positive will be excluded. 20. Evidence of other clinically significant uncontrolled condition(s) including but not limited to, uncontrolled systemic bacterial, viral including CMV, fungal or parasitic infection (except for fungal nail infection), or other clinically significant active disease process which in the opinion of the investigator and IND sponsor may pose a risk for patient participation. Screening for chronic conditions is not required. 21. Prolongation of the QT interval corrected for heart rate (QTcF) \> 470 msec on one electrocardiograms (ECGs), during Screening. EKG might be repeated same day to check for any physiologic variation. QTcF is calculated using Fridericia's Formula (QTcF): QTcF = QT/(RR0.33). 22. Correction of suspected drug induced QTcF prolongation can be attempted at the investigator's discretion and only if clinically safe to do so with either discontinuation of the offending drug or switch to another drug not known to be associated with QTcF prolongation. 23. Correction for underlying bundle branch block (BBB) allowed. Note: Participants with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker. 24. Concomitant malignancies or previous malignancies with less than a 1-year disease-free interval at the time of signing consent. Subjects with adequately treated basal or squamous cell carcinoma of the skin, or adequately treated carcinoma in situ (e.g. cervix) may enroll irrespective of the time of diagnosis. Patients with controlled, advanced prostate cancer (not on active chemotherapy) are permitted. Active second malignancy unless in remission with life expectancy \> 1 years. Examples include: 1. Adequately treated no melanomatous skin cancer or lentigo maligna melanoma without current evidence of disease. 2. Adequately treated cervical carcinoma in situ without current evidence of disease. 3. Localized (e.g., lymph node negative) breast cancer treated with curative intent with no evidence of active disease present for more than 3 years and receiving adjuvant hormonal therapy. 4. Localized prostate cancer undergoing hormonal therapy. 25. Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction. 26. With known allergies to xanthine oxidase inhibitors and/or rasburicase. 27. Other severe acute or chronic medical or psychiatric condition or laboratory abnormality that, in the opinion of the investigator, may increase the risk associated with study participation or study treatment administration or may interfere with the interpretation of study results and/or would make the participant inappropriate for enrollment into this study. 28. No concomitant anticancer therapies, immunotherapies, cellular, or radiotherapy. No major surgery within 4 weeks prior to first dose of study treatment. 29. Uncontrolled autoimmune hemolytic anemia (AIHA) or immune thrombocytopenia. Active uncontrolled auto-immune cytopenia (e.g., autoimmune hemolytic anemia \[AIHA\], idiopathic thrombocytopenic purpura \[ITP\]) is for which new therapy was introduced or existing therapy was escalated within the 4 weeks prior to study enrollment to maintain adequate blood counts. 30. Concomitant steroids for disease related pain control are allowed at any dose but must be discontinued prior to any study treatment initiation. Chronic use of corticosteroids is allowed up to 20 mg prednisone or equivalent daily for non-cancer related conditions at the time of study start. 31. History of GVHD, allogeneic HSCT transplant, allogeneic organ transplant 32. Any serious medical condition including but not limited to, uncontrolled hypertension, diabetes mellitus, active/symptomatic coronary artery disease, COPD, renal failure, active infection, active hemorrhage, laboratory abnormality, or psychiatric illness that places the participant at unacceptable risk and would prevent the subject from signing the informed consent form.