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 associated with QTcF prolongation. Correction for underlying bundle branch block (BBB) allowed. Note: Patients with pacemakers are eligible if they have no history of fainting or clinically relevant arrhythmias while using the pacemaker * Evidence of active uncontrolled/untreated infection (viral, bacterial, fungal, opportunistic) of any origin. * Participants with active immunologic or inflammatory/autoimmune disease affecting the CNS, and unrelated to their disease under study or previous treatment. * Patients with active CNS involvement of Mantle Cell Lymphoma. A history of CNS Mantle Cell Lymphoma is allowed, as long as it has cleared, and the patient is able to comply with study procedures. Patients with previous treatment for CNS involvement who are neurologically stable and without evidence of disease may be eligible with documented Sponsor approval. * Known positive Human immunodeficiency virus (HIV) status. For patients with unknown HIV status, HIV testing will be performed at Screening and result must be negative for enrollment. * Hepatitis B virus (HBV): Patients with positive hepatitis B surface antigen (HBsAg) are excluded. Patients with positive hepatitis B core antibody (anti-HBc) and negative HBsAg require a negative hepatitis B polymerase chain reaction (PCR) evaluation before randomization. Patients who are HBV DNA PCR positive will be excluded. Patients who are HBV DNA PCR negative with positive anti-HBc require prophylaxis against Hepatitis B reactivation (see Section 6.4 "General Guidance for Hepatic Monitoring"). * Hepatitis C virus (HCV): positive hepatitis C antibody. If positive hepatitis C antibody result, patient will need to have a negative result for hepatitis C ribonucleic acid (RNA) before randomization. Patients who are hepatitis C RNA positive will be excluded. * Known active cytomegalovirus (CMV) infection. Unknown or negative status are eligible. * Participants who require the concurrent use of chronic systemic steroids or immunosuppressant medications. Steroids should not be given within 5 days prior to leukapheresis. Concomitant bridging steroids (section 6.6) are allowed after leukapheresis. * Known hypersensitivity or severe reaction to pirtobrutinib, similar compounds, or excipients. * Participants who have not recovered from adverse events (AEs) due to prior anticancer therapy (i.e., have residual toxicities \> Grade 1), with the exception of stable Grade 2 peripheral neuropathy and/or any grade alopecia. * Pregnant or nursing (breast-feeding) women are excluded from this study because there is an unknown but potential risk to using pirtobrutinib in pregnant or nursing women. Patients are excluded if they are pregnant or plan to become pregnant during the study or within 1 year of the last dose of study treatment. Patients are also excluded if they are lactating or plan to breastfeed during the study or within 1 week of the last dose of study treatment. Please see Section 4.3 and Section 4.4 for General Guidance for Women of Child Bearing Potential and/or Use of Contraceptive Methods. * Any condition that would, in the investigator's judgement, interfere with full participation in the study, including administration of pirtobrutinib and attending required study visits (if outpatient); pose a significant risk to the participant; or interfere with interpretation of study data. * Inability of the participant to swallow and retain oral medication. Or, if there is clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal (GI) absorption of the study drug. * Patients 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) * Major surgery within 4 weeks prior to enrollment. * History of a previously diagnosed hereditary bleeding disorder. * Patients requiring therapeutic anticoagulation with warfarin or another vitamin K antagonist. * Active second malignancy unless in remission and with life expectancy \> 2 years. * Vaccination with live vaccine within 28 days prior to randomization. * History of stroke or intracranial hemorrhage within 6 months of enrollment. * History of allogeneic or autologous stem cell transplant within 60 days of enrollment, presence of either of the following regardless of prior stem cell transplant timing: active graft vs. host disease; cytopenias from incomplete blood cell count recovery post-transplant. * Active uncontrolled autoimmune cytopenia, including autoimmune hemolytic anemia or idiopathic thrombocytopenic purpura for which new therapy was introduced or existing therapy was escalated within the 4 weeks prior to study enrollment to maintain adequate blood counts.