Phase 2 Open Label Randomized Study of Pirtobrutinib and Brexucabtagene Autoleucel in R/R MCL

Inclusion Criteria: * Patients with a histologically confirmed diagnosis of mantle cell lymphoma (MCL) will be eligible. * Adult males or females who are 18 years of age or older at time of signing informed consent. * Must have ability to comprehend and the willingness to sign written informed consent for study participation. * Eligible to receive CAR T-cell therapy (Brexucabtagene autoleucel) for MCL by the standard of care label, which states: "TECARTUS or Brexucabtagene autoleucel is a CD19-directed genetically modified autologous T-cell immunotherapy indicated for the treatment of: Adult patients with relapsed or refractory mantle cell lymphoma (MCL)" * ECOG performance status 0 to 2. * Patients are required to have the following washout periods prior to leukapheresis. In addition, prior treatment-related AEs must have recovered to Grade ≤ 1 with the exception of alopecia and Grade 2 peripheral neuropathy. * Targeted agents (i.e. BTK inhibitors), investigational agents, therapeutic monoclonal antibodies or cytotoxic chemotherapy: 5 half-lives or 2 weeks, whichever is shorter * Antibody-drug conjugates (ADC): 10 weeks * Radiation therapy: Broad field radiation (≥ 30% of the bone marrow or whole brain radiotherapy): 14 days. Palliative limited field radiation: 7 days. Note: In the case of known central nervous system (CNS) involvement by systemic lymphoma: Patients with previous treatment for CNS involvement who are neurologically stable and without evidence of disease may be eligible if a compelling clinical rationale is provided by the Investigator and with documented Sponsor approval. * Bendamustine or other purine analogues: 3 months. * Corticosteroids: 5 days * The effects of Pirtobrutinib on the developing human fetus are unknown. For this reason and because other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation as outlined in criteria below: * Men must agree to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through safety follow up and must refrain from donating sperm during this period. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the participants in their understanding confirmed. * Willingness of women of reproductive potential and their partners to observe highly effective birth control methods for the duration of treatment and for 1 month following the last dose of study treatment (see Section 4.3 and Section 4.4 for further details) * Women of childbearing potential must have a negative serum pregnancy test at screening and before the first dose of pirtobrutinib and must agree to take appropriate precautions to avoid pregnancy (with at least 99% certainty) from screening through safety follow up. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the participants and their understanding confirmed. * Women of non-childbearing potential (i.e. surgically sterile with a hysterectomy and/or bilateral oophorectomy OR \>= 12 months of amenorrhea) are eligible. * Patients must meet the following laboratory parameters at screening: * Hematology (criteria the same regardless of bone marrow involvement; must be independent of transfusions and G-CSF support within 7 days of assessment) * Platelets \>= 50 x 10\^9/L * Hemoglobin \>= 8g/dL * Absolute Neutrophil Count \>=1.0 x 10\^9/L * Hepatic * ALT \< 2.5 x ULN for age, \<5 x ULN in the presence of liver metastases * AST \< 2.5 x ULN for age, \<5 x ULN in the presence of liver metastases * Total bilirubin \< 1.5 x ULN or \<3 x ULN in the presence of documented Gilbert's syndrome unconjugated hyperbilirubinemia) * Renal Creatinine clearance \>= 30 mL/minute based on Cockcroft-Gault formula. * Cardiopulmonary Cardiac LVEF \>=40% confirmed by ECHO/multigated analysis * Adequate pulmonary function \<= Grade 2 dyspnea and \<= Grade 2 hypoxia per CTCAE v5.0. * Adequate coagulation, defined as activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) and prothrombin (PT) or (international normalized ratio (INR) not greater than 1.5 x ULN. Exclusion Criteria: * Patients who have previously received treatment with pirtobrutinib for \>2 months prior to study enrollment are ineligible. Patients who are relapsed or refractory and then received less than 2 months of pirtobrutinib as "holding therapy" while awaiting CAR T-cell therapy evaluation, and who did not demonstrate disease progression while on pirtobrutinib holding therapy, are eligible. * Patients who have previously discontinued pirtobrutinib due to disease progression, intolerance, or toxicity. * Patients who are currently receiving or who have received any investigational study agent ≤4 weeks prior to screening visit are ineligible. * Prior treatment with chimeric antigen receptor (CAR) T-cell therapy. * Participants with clinically significant or uncontrolled cardiac disease, including unstable angina or acute coronary syndrome within the past 2 months prior to randomization, history of myocardial infarction within 3 months prior to randomization, documented LVEF by any method of ≤ 40% in the 12 months prior to randomization, or ≥ Grade 3 NYHA functional classification system of heart failure. * Uncontrolled or symptomatic arrhythmias, including prolongation of the QT interval corrected for heart rate (QTcF) \> 470 msec. QTcF is calculated using Fridericia's Formula (QTcF): QTcF = QT/(RR0.33). 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 assoc