Study of Brexucabtagene Autoleucel (KTE-X19) for the Treatment of Individuals With Relapsed/Refractory B-Cell Malignancies

Key Inclusion Criteria: Cohort 1: * Pathologically confirmed mantel cell lymphoma (MCL), with documentation of either overexpression of cyclin D1 or presence of t(11;14) * Received at least one prior regimen for MCL. Prior therapy must have included: * Anthracycline or bendamustine-containing chemotherapy, or * Anti-CD20 monoclonal antibody therapy, or * Treatment with Bruton's tyrosine kinase inhibitor (BTKi): ibrutinib, acalabrutinib, or a BTKi in a clinical trial for r/r MCL. * Relapsed or refractory disease, defined by the following: * Disease progression after last regimen, or * Failure to achieve a partial response (PR) or complete response (CR) to the last regimen * Magnetic resonance imaging (MRI) of the brain showing no evidence of central nervous system (CNS) lymphoma * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * Absolute neutrophil count (ANC) ≥ 1,000/uL * Platelet count ≥ 75,000/uL * Absolute lymphocyte count ≥ 100/uL * Adequate renal, hepatic, pulmonary, and cardiac function defined as the following: * Creatinine clearance (as estimated by Cockcroft Gault formula) ≥ 60 cc/min * Serum alanine aminotransferase/aspartate aminotransferase (ALT)/AST) ≤ 2.5 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 mg/dl, except in individuals with Gilbert's syndrome * Cardiac ejection fraction ≥ 50%, no evidence of pericardial effusion (except trace or physiological) as determined by an echocardiogram (ECHO), and no clinically significant electrocardiogram (ECG) findings * No clinically significant pleural effusion * Baseline oxygen saturation \> 92% on room air * Females of childbearing potential must have a negative serum or urine pregnancy test. Females who have undergone surgical sterilization or who have been post-menopausal for at least 2 years are not considered to be of childbearing potential. * At least 1 measurable lesion. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. If the only measurable disease is lymph node disease, at least 1 lymph node should be ≥ 2 cm. Cohort 2: * Individuals whose commercial manufacture of KTE-X19 did not meet commercial release specification(s) Key Exclusion Criteria: Cohort 1: * Presence or suspicion of fungal, bacterial, viral, or other infection that is uncontrolled or requiring intravenous (IV) antimicrobials for management. * History of human immunodeficiency virus (HIV) infection or acute or chronic active hepatitis B or hepatitis C infection. * History of detectable cerebrospinal fluid (CSF) malignant cells or brain metastases or with a history of CNS lymphoma, CSF malignant cells, or brain metastases * History of CNS disorder, such as seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, cerebral edema, posterior reversible encephalopathy syndrome, or any autoimmune disease with CNS involvement Cohort 2: * Any medical condition that, as deemed by the treating physician, may interfere with assessment of safety or efficacy of study treatment Note: Other protocol defined Inclusion/Exclusion criteria may apply.