Pembrolizumab, Ibrutinib, and Rituximab for PCNSL

Inclusion Criteria: * Participant must be able to understand and willing to sign a written informed consent document. * Participant must have signed and dated an IRB/IEC approved written informed consent form in accordance with regulatory and institutional guidelines. This must be obtained before the performance of any protocol-related procedures that are not part of normal subject care. * Participant must be willing and able to comply with scheduled visits, treatment schedule, laboratory tests, and other requirements of the study. * Participant must be at least 18 years old on day of signing informed consent. * Subjects with pathologically confirmed PCNSL who progressed after CNS-directed therapy, primary refractory disease and relapsed disease are allowed. Participants should have evidence of R/R disease on MRI or CSF cytology. Ocular only recurrences are allowed. * Subjects must have a Eastern Cooperative Oncology Group (ECOG) performance status of 0-1. * Life expectancy of \>3 months (in the opinion of the investigator) * Toxicities due to prior therapy must be stable and recovered to ≤ Grade 1 * Must be able to tolerate lumbar puncture and/or Ommaya taps * Demonstrate adequate organ function as defined below, all screening labs should be performed within 28 days of treatment initiation. * Hematology * White Blood Count (WBC) ≥ 2 K/μL * Platelet count ≥ 100 K/μL * Absolute Neutrophil Count ≥ 1.5 K/μL * Hemoglobin \> 9.0 g/dL or ≥ 5.6 mmol/L (Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks) * Biochemistry * Serum creatinine ≤1.5 x institutional ULN OR Measured or calculated creatinine clearance ≥30 mL/min for participant with creatinine levels \>1.5 × institutional ULN (Creatinine clearance should be calculated per institutional standard) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN(≤5 × ULN for participants with liver metastases) * Total bilirubin (TBILI) ≤ 1.5 x institutional ULN (except subjects with Gilbert Syndrome who must have a total bilirubin level of \< 3.0 x institutional ULN) OR Direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN) * Coagulation studies * INR OR PT and Activated aPTT ≤1.5 × institutional ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * Women of child-bearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant, must have a negative serum pregnancy test within 72 hours prior to registration. * Women in the following categories are not considered WOCBP: * Premenarchal * Premenopausal female with 1 of the following: * Documented hysterectomy * Documented bilateral salpingectomy * Documented bilateral oophorectomy * Note: Documentation can come from the site personnel's review of the participant's medical records, medical examination, or medical history interview. * Postmenopausal female: A postmenopausal state is defined as no menses for 12 months without an alternative medical cause. * A high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a postmenopausal state in women not using hormonal contraception or hormonal replacement therapy (HRT). However, in the absence of 12 months of amenorrhea, confirmation with two FSH measurements in the postmenopausal range is required. * Females on HRT and whose menopausal status is in doubt will be required to use one of the non-hormonal highly effective contraception methods if they wish to continue their HRT during the study. Otherwise, they must discontinue HRT to allow confirmation of postmenopausal status before study enrollment. * Women of child-bearing potential (WOCBP; see definition above), must agree to use a highly effective method of contraception consistently and correctly as described below during study treatment and for 120 days after study discontinuation. * 1\. Highly Effective Contraceptive Methods That Are User Dependent a (Failure rate of \< 1% per year when used consistently and correctly.) * a. Combined (estrogen- and progestogen- containing) hormonal contraception b, c * i. Oral * ii. Intravaginal * iii. Transdermal * iv. Injectable * b. Progestogen-only hormonal contraception b, c * i. Oral * ii. Injectable * 2\. Highly Effective Methods That Have Low User Dependency (Failure rate of \<1% per year when used consistently and correctly) * a. Progestogen- only contraceptive implant b, c * b. Intrauterine hormone-releasing system (IUS) b * c. Intrauterine device (IUD) * d. Bilateral tubal occlusion * e. Vasectomized partner: A vasectomized partner is a highly effective contraception method provided that the partner is the sole male sexual partner of the WOCBP and the absence of sperm has been confirmed. If not, an additional highly effective method of contraception should be used. * f. Sexual abstinence: Sexual abstinence is considered a highly effective method only if defined as refraining from heterosexual intercourse during the entire period of risk associated with the study treatment. The reliability of sexual abstinence needs to be evaluated in relation to the duration of the study and the preferred and usual lifestyle of the participant. * NOTES: Use should be consistent with local regulations regarding the use of contraceptive methods for participants of clinical studies. * Typical use failure rates are lower than perfect-use failure rates (i.e. when used consistently and correctly). * If hormonal contraception efficacy is potentially decreased due to interaction with study treatment, condoms must be used in addition to the hormonal contraception during the treatment period and for at least during study treatment and for 120 days after study discontinuation after the last dose of study treatment. * If locally required, in accordance with Clinical Trial Facilitation Group (CTFG) guidelines, acceptable contraceptive implants are limited to those which inhibit ovulation. * Male participants must agree to use at least one of the following methods of contraception starting with the first dose of study therapy through 120 days after the last dose of therapy: * 1\. Be abstinent from penile-vaginal intercourse as their usual and preferred lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent * 2\. Use a male condom plus partner use of a contraceptive method with a failure rate of \<1% per year as described in Eligibility criterion 3.1.13 when having penile-vaginal intercourse with a woman of childbearing potential who is not currently pregnant. * a. 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 penetration. Exclusion Criteria: Participants who meet any of the following criteria will not be eligible for admission into the study. * Patients who cannot undergo MRI brain * Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40,CD137) * Previously progressed on ibrutinib or other BTK inhibitor use (patient who have previously received BTK inhibitor but not progressed while on it are allowed) * Patients with \> Grade 2 intracranial hemorrhage * Concomitant warfarin, any other warfarin-derivative anticoagulant, vitamin K antagonists, within 7 days before starting treatment. Note: novel oral anticoagulants (NOACs, e.g., Apixaban, Dabigatran, Edoxaban, Rivaroxaban), low molecular weight heparin (LMWH) are allowed * Arterial thromboembolic events such as cerebrovascular accident within 3 months before the start of study treatment * Active autoimmune disease requiring immunosuppressive agents or steroids (prednisone \>10mg or equivalent) * Has 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).Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Requires treatment for PCNSL with high dose systemic corticosteroids defined as dexamethasone \> 4 mg/day or bioequivalent for \>3 consecutive days within 2 weeks of registration * Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks \[could consider shorter interval for kinase inhibitors or other short half-life drugs\] prior to dosing. OR 5 half-lives, whichever is shorter --- Note: Participants must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants with≤Grade 2 neuropathy may be eligible. * Patients who underwent major surgery ≤ 2 weeks before starting study treatment are excluded. If participant underwent major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. Patients who plan to undergo surgery within 2 weeks of first dose of study treatment are excluded. * Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. Has received prior radiotherapy to CNS disease within 2 weeks of start of study treatment. * Has received a live vaccine within 30 days prior to the first dose of study drug. 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 (eg, FluMist®) are live attenuated vaccines and are not allowed. * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, transitional cell carcinoma of urothelial cancer, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Has severe hypersensitivity (≥ Grade 3) to study agents and/or any of its excipients. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Patient is known to have an uncontrolled active systemic infection (\>CTCAE grade 2) and recent infection requiring intravenous anti-infective treatment that was completed ≤14 days before the first dose of study drug. * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure (New York Heart Association \> Class 2), unstable angina, or myocardial infarction within 6 months of screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification * Uncontrolled hypertension despite optimal medical management (per investigator's assessment). * Patient has poorly controlled diabetes mellitus with a glycosylated hemoglobin \>8% or poorly controlled steroid-induced diabetes mellitus with a glycosylated hemoglobin of \>8%. * Non-healing wound, ulcer or bone fracture. * Known bleeding diathesis (eg, von Willebrand's disease) or hemophilia. * Unable to swallow capsules or disease significantly affecting gastrointestinal function, such as malabsorption syndrome, resection of the stomach or small bowel, or complete bowel obstruction. * Concurrent administration of medications or foods that are moderate or strong inhibitors or strong inducers of cytochrome P450 (CYP) 3A4/5 (need to be discontinued 2 weeks before starting study treatment) * Enzyme-inducing antiepileptic drugs (EIAED) need to be discontinued and switched to a non-EIAED 2 weeks prior to starting on trial drugs * Has known history of HIV/AIDS * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. * Has a known history of active TB (Bacillus Tuberculosis) * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) * Patients who have undergone prior allogeneic stem cell transplant * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment