Study of KTE-X19 in Adult Japanese Participants With Relapsed/Refractory Mantle Cell Lymphoma or Relapsed/Refractory B-precursor Acute Lymphoblastic Leukemia

Key Inclusion Criteria: MCL Cohort: * Pathologically confirmed MCL, with documentation of either overexpression of cyclin D1 or presence of t(11;14) * Up to 5 prior regimens for MCL. Prior therapy must have included: * Anthracycline-, bendamustine-, or high-dose cytarabine- containing chemotherapy, and * Anti-CD20 monoclonal antibody therapy, and * Bruton's tyrosine kinase inhibitor (BTKi) * Relapsed or refractory disease, defined by the following: * Disease progression after last regimen, or * Refractory disease is defined failure to achieve partial response (PR) or complete remission (CR) to the last regimen * 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 ALL Cohort: * Relapsed or refractory B-ALL defined as one of the following: * Relapsed or refractory disease after one line of systemic therapy; * Primary refractory, or * First relapse if first remission ≤ 12 months * Relapsed or refractory disease after two or more lines of systemic therapy * Relapsed or refractory disease after allogeneic transplant provided individuals is at least 100 days from SCT at the time of enrollment and off of immunosuppressive medications for at least 4 weeks prior to enrollment * Morphological disease in the bone marrow (\> 5% blasts) * Individuals with Philadelphia-positive (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 Key Exclusion Criteria: MCL Cohort: * History of malignancy other than nonmelanomatous skin cancer or carcinoma in situ (eg, cervix, bladder, breast) unless disease-free for at least 3 years * Autologous SCT (autoSCT) within 6 weeks of planned KTE-X19 infusion * History of alloSCT with the exception of individuals with no donor cells detected on chimerism \> 100 days after alloSCT * Prior CD19 targeted therapy * Prior CAR therapy or other genetically modified T-cell therapy * History of hypersensitivity to any of the ingredients of KTE-X19 or to any of the animal-derived ingredients (bovine and rodent) used in the manufacturing process of KTE-X19 ALL Cohort: * Diagnosis of Burkitt's leukemia/lymphoma according to World Health Organization (WHO) classification or chronic myelogenous leukemia lymphoid blast crisis * History of malignancy other than non-melanoma skin cancer or carcinoma in situ (eg, cervix, bladder, breast) unless disease free for at least 3 years * History of hypersensitivity to any of the ingredients of KTE-X19 or to any of the animal-derived ingredients (bovine and rodent) used in the manufacturing process of KTE-X19 Note: Other protocols defined Inclusion/Exclusion criteria may apply.