Pembro Plus CAR T-cell Therapy in R/R in PMBCL

Inclusion Criteria: * Histologically confirmed diagnosis of PMBCL, EBV+ DLBCL or THRLBCL at one of the participating institutions. * Availability of archival or freshly collected tumor tissue before study enrollment. If archival tissue is unavailable or is determined to be inadequate, tumor tissue must be obtained from a biopsy performed at screening, unless an exception is given after consultation with the sponsor-investigator. * Eligible for standard of care CAR T-cell therapy with progression after at least two prior lines of therapy OR refractory to initial chemoimmunotherapy OR relapse within 12 months of front-line chemoimmunotherapy OR one prior line of therapy and not fit for HSCT. * ECOG Performance Status of 0 or 1. * Left ventricular ejection fraction (LVEF) ≥ 50% on cardiac multiple-gated acquisition (MUGA) scan or cardiac echocardiogram (ECHO). * Adequate hematologic function (unless due to underlying disease, as established for example, by extensive bone marrow involvement or due to hypersplenism secondary to the involvement of the spleen by lymphoma per the investigator), defined as follows: * ANC ≥ 1,000/μL * Hemoglobin ≥ 8 g/dL * Platelet count ≥ 50,000/μL * Participants must have adequate organ as defined below: * Total bilirubin ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN * AST(SGOT)/ALT(SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver involvement) * Adequate renal function defined by serum creatinine ≤1.5 x ULN or creatinine clearance (by Cockcroft-Gault) ≥ 40 ml/min for patients with serum creatinine \>1.5 x ULN * At least one bi-dimensionally FDG-avid measurable lymphoma lesion on PET/CT scan, defined as ≥ 1.5 cm in its longest dimension on CT scan, or ≥ 1 cm if extranodal (and measurable). * Women of childbearing potential (WOCBP) and men must agree to use effective contraception when sexually active. This applies for the time period between signing of the informed consent form and 6 months for WOCBP and for men after the last administration of study treatment. A woman is considered of childbearing potential, i.e. fertile, following menarche and until becoming post-menopausal unless permanently sterile. Permanent sterilization methods include but are not limited to hysterectomy, bilateral salpingectomy and bilateral oophorectomy. A postmenopausal state is defined as no menses for continuous 12 months without an alternative medical cause. A high follicle stimulating hormone (FSH) level in the postmenopausal range may be used to confirm a post-menopausal state in women not using hormonal contraception or hormonal replacement therapy. The investigator or a designated associate is requested to advise the patient how to achieve highly effective birth control, e.g. intrauterine device (IUD), intrauterine hormone-releasing system (IUS), bilateral tubal occlusion, vasectomized partner, use of two forms of birth control, and sexual abstinence. The use of condoms by male patients is required unless the female partner is permanently sterile. * Age ≥18 years. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients in urgent need of cytoreductive therapy. * Participants who are receiving any other investigational agents. * History of other malignancies, except: * Malignancy treated medically or surgically with curative intent and with no known active disease present for ≥2 years before study registration * Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease * Adequately treated carcinoma in situ without evidence of disease. * Localized prostate cancer and low-risk prostate cancer on active surveillance * In the opinion of the treating investigator, there is limited potential to interfere with the safety or efficacy of the investigational regimen. Such exceptions must be approved by the Sponsor-Investigator. * Has received a live vaccine within 30 days prior to study registration. 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. * Less than 6 months of response to prior PD-L1 inhibitor or PD-1 inhibitor or grade 3 or higher immune-related adverse events. * Prior treatment with CAR T-cell therapy. * Lactating or pregnant. Women of childbearing potential (WOCBP) must have a negative pregnancy test (urine or serum) at screening. WOCBP will require a negative pregnancy test within 72 hours prior to starting treatment, but eligibility for study enrollment may be confirmed based on testing at screening. * Known active lymphomatous involvement of the central nervous system. History of prior CNS involvement is allowed. * Recent infection requiring intravenous antibiotics that was completed ≤7 days before the first dose of study drug, or any uncontrolled active systemic infection. * Has a known history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus infection. * History of Human immunodeficiency virus (HIV)-infection. * Has received prior radiotherapy within 2 weeks of study registration. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. * Has received prior systemic anti-cancer therapy within 2 weeks or investigational agents within 4 weeks. * Significant liver disease, such as hepatitis (viral or non-viral) or cirrhosis * Prior macrophage activation syndrome (MAS) or hemophagocytic lymphohistiocytosis (HLH) * Uncontrolled arrhythmia or Class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months of enrollment. * Known history of central nervous system or neurologic disease including stroke or intracranial hemorrhage within 3 months prior to enrollment or seizure disorder. Prior CNS involvement with lymphoma is allowed if previously treated with no evidence of involvement at study entry. * Prior solid organ or allogeneic stem cell transplant or within 6 weeks of autologous stem cell transplant. * 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). * 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 study registration. Replacement therapy (eg., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. * Active pneumonitis or interstitial lung disease. * Severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. * Has a history or current evidence of any condition, therapy, or laboratory abnormality 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. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Has not met requirements for standard of care CAR-T therapy