Acalabrutinib + Liso-Cel In R/R Aggressive B-Cell Lymphomas

Inclusion Criteria: * Adult patients ≥18 years with histologically confirmed aggressive B-cell NHL including diffuse large B-cell lymphoma (DLBCL), either de novo or transformed from any indolent B-cell lymphoma, and including DLBCL NOS, T cell/histiocyte-rich large B-cell lymphoma, Epstein-Barr virus \[EBV\] positive DLBCL NOS, primary mediastinal \[thymic\] large B-cell lymphoma (PMBCL), high grade B-cell lymphoma NOS, or high grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements \[double/triple hit lymphoma (DHL/THL)\]; and grade 3B follicular lymphoma. Patients with primary CNS lymphoma are not eligible. Patients with secondary CNS involvement by lymphoma are eligible if they otherwise meet all eligibility criteria. * Relapsed or refractory to at least 2 prior lines of systemic lymphoma therapy. Previous therapy must have included a CD20-targeted agent and an anthracycline or alkylating agent. * PET-positive measurable disease * ECOG Performance status 0-2 * Estimated creatinine clearance of ≥30 mL/min, calculated using the Cockcroft and Gault equation (if male, \[140Age\] x Mass \[kg\] / \[72 x creatinine g/dL\];multiply by 0.85 if female) * Alanine Aminotransferase (ALT) \<= 2.5 times the ULN * Bilirubin \<= 2 x ULN (or \<= 3.0 mg/dL for patients with Gilbert-Meulengracht syndrome or lymphomatous involvement of the liver) * Hemodynamically stable and Left Ventricle Ejection Fraction (LVEF) \>= 40% confirmed by echocardiogram or Multigated Radionuclide Angiography (MUGA) * For subjects with atrial fibrillation, atrial fibrillation must be controlled and asymptomatic * Absolute neutrophil count (ANC) \>= 1000/mm3 * Platelets \>= 50,000/mm3 * Adequate pulmonary function, defined as \<= CTCAE Grade 1 dyspnea and SaO2 \> 91% on room air * Adequate vascular access for leukapheresis procedure (either peripheral line or surgically-placed line) * Woman of childbearing potential (WOCBP) who are sexually active must use highly effective methods of contraception during treatment and for 2 days after the last dose of acalabrutinib. * Willing and able to participate in all required evaluations and procedures in this study protocol. * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information. Exclusion Criteria: * Another active malignancy which requires concurrent cancer-directed therapy * Previous treatment with gene therapy product or adoptive T cell therapy * Allogeneic stem cell transplant within 90 days of leukapheresis * Active acute or chronic GVHD * HIV infection * Serologic status reflecting active hepatitis B or C infection * Subjects who are hepatitis B core antibody (anti-HBc) positive and who are hepatitis B surface antigen (HBsAg) negative will need to have a negative PCR result before enrollment and must be willing to undergo DNA PCR testing during the study. Those who are HbsAg-positive or hepatitis B PCR positive will be excluded. * Subjects who are hepatitis C antibody positive will need to have a negative PCR result before enrollment. Those who are hepatitis C PCR positive will be excluded. * Uncontrolled infection * Clinically relevant CNS pathology * History of cardiovascular conditions within the past 6 months, including class III or IV heart failure as defined by New York Heart Association (NYHA), cardiac angioplasty or stenting, myocardial infarction, unstable angina, or clinically significant arrhythmias: Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants should be class 2B or better. * Autoimmune disease requiring chronic systemic corticosteroids at a dose of greater than 10 mg of prednisone daily or an equivalent dose of another corticosteroid * Treatment with alemtuzumab within 6 months leukapheresis or fludarabine or cladribine within 3 months of leukapheresis * Therapeutic anticoagulation * Bleeding diathesis * Has difficulty with or is unable to swallow oral medication, or has significant gastrointestinal disease that would limit absorption of oral medication. * Known history of hypersensitivity or anaphylaxis to study drug(s) including active product or excipient components. * Presence of a gastrointestinal ulcer diagnosed by endoscopy within 3 months before screening. * Requires treatment with a strong cytochrome P450 3A4 (CYP3A4) inhibitor/inducer. * Prothrombin time (PT)/INR or aPTT (in the absence of lupus anticoagulant) \>2x ULN. * Requires treatment with proton pump inhibitors (eg, omeprazole, esomeprazole, lansoprazole, dexlansoprazole, rabeprazole, or pantoprazole). Note: Subjects receiving proton pump inhibitors who switch to H2-receptor antagonists or antacids are eligible for enrollment to this study. * History of significant cerebrovascular disease/event, including stroke or intracranial hemorrhage, within 6 months before the first dose of study drug. * Major surgical procedure within 28 days of first dose of study drug. Note: If a subject had major surgery, they must have recovered adequately from any toxicity and/or complications from the intervention before the first dose of study drug. * Breastfeeding or pregnant: Pregnant women are excluded from this study because acalabrutinib is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with acalabrutinib, breastfeeding should be discontinued if the mother is treated with acalabrutinib.