Study Evaluating Brexucabtagene Autoleucel (KTE-X19) in Pediatric and Adolescent Participants With Relapsed/Refractory B-precursor Acute Lymphoblastic Leukemia or Relapsed/Refractory B-Cell Non-Hodgkin Lymphoma

Key Inclusion Criteria for the ALL Cohort * Relapsed or refractory B-precursor ALL defined as one of the following: * Primary refractory disease * Any relapse within 18 months after first diagnosis * Relapsed or refractory disease after 2 or more lines of systemic therapy * Relapsed or refractory disease after allogeneic transplant provided individual is at least 100 days from stem cell transplant at the time of enrollment * Disease burden defined as at least 1 of the following: * Morphological disease in the bone marrow (\> 5% blasts) * Minimal/Measurable Residual Disease (MRD) positive (threshold 10\^-4 by flow or Polymerase chain reaction (PCR)) * Individuals with Ph+ disease are eligible if they are intolerant to tyrosine kinase inhibitor (TKI) therapy, or if they have relapsed/refractory disease despite treatment with at least 2 different TKIs * Age ≤ 21 years and weight ≥ 6 kg at the time of assent or consent per Institutional Review Board (IRB) guidelines * Lansky (age \< 16 years at the time of assent/consent) or Karnofsky (age ≥ 16 years at the time of assent/consent) performance status ≥ 80 at screening * Adequate renal, hepatic, pulmonary and cardiac function defined as: * Creatinine clearance (as estimated by Cockcroft Gault or Schwartz) ≥ 60 mL/min * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 5 x upper limit of normal (ULN) * Total bilirubin ≤ 1.5 x ULN, except in individuals with Gilbert's syndrome * Left vent…