A Study of CD19 Targeted CAR T Cell Therapy in Pediatric Patients With Relapsed or Refractory B Cell Acute Lymphoblastic Leukemia (B ALL) and Aggressive Mature B-cell Non-Hodgkin Lymphoma (B NHL)

INCLUSION CRITERIA: * Male or female patients \< 18 years old at screening * Patients with ≥ 6 kg body weight at screening B ALL Cohort: r/r CD19-positive B ALL defined as: 1. Primary refractory disease defined as: 1. National Cancer Institute high risk (defined as presenting with white blood cell count ≥ 50 × 10\^9 cells/L or aged ≥ 10 years at diagnosis) patients with MRD ≥ 0.01% after first-line induction and consolidation and blinatumomab (if allowed per country specific approvals and treatment guidelines). 2. Refractory B ALL if BM disease ≥ 25% after first line induction and consolidation. 3. KMT2A rearranged infant ALL with MRD ≥ 1% after first line induction and blinatumomab (if allowed per country specific approvals and treatment guidelines) or MRD ≥ 0.01% after first line induction and consolidation. 2. First relapse 1. Children's Oncology Group high risk first relapse involving BM \< 36 months after initial diagnosis or an isolated extramedullary relapse \< 18 months after initial diagnosis. 2. Patients with Down syndrome and infants with KMT2A rearranged are eligible with first relapse at any time. 3. Refractory disease with MRD ≥ 0.01% after re-induction for first relapse (with or without blinatumomab, if allowed per country specific approvals and treatment guidelines). 3. Second or greater relapse 4. Relapsed or refractory post-SCT: a. Relapsed or refractory disease after allogeneic transplant provided obe cel infusion occurs ≥ 3 months after SCT. 5. Philadelphia chromosome positive (Ph+) ALL: 1. Any of the above with Ph+ ALL where patient is intolerant to or has failed at least one tyrosine kinase inhibitor (TKI) or if TKI therapy is contraindicated. B NHL Cohort: r/r CD19-positive aggressive mature B NHL defined as 1 of the following: 1. Relapsed after one or more prior therapies (can include allogeneic and autologous hematopoietic SCT). 2. Primary refractory (have not achieved a CR or PR after the first line of therapy) with measurable, disease by radiological criteria at screening including the B NHL subtypes: (i) diffuse large B-cell lymphoma (DLBCL), (ii) Burkitt's lymphoma, (iii) primary mediastinal large B-cell lymphoma (PMBCL) and (iv) high-grade B-cell lymphoma (not otherwise specified). * Karnofsky (age ≥ 10 years) or Lansky (age \< 10 year) performance status score ≥ 50%. * In patients with B ALL, local documentation of CD19 expression on leukemic blasts in the BM, peripheral blood, or cerebrospinal fluid (CSF) or biopsy done no more than 30 days prior to consent. In patients treated with blinatumomab, testing should be undertaken after blinatumomab therapy has been stopped. In patients with mature B NHL, CD19 expression must be confirmed in a biopsy after any CD19 targeted therapies. * Adequate renal, hepatic, pulmonary, and cardiac function. EXCLUSION CRITERIA: * Diagnosis of chronic myelogenous leukemia lymphoid in blast crisis. * History or presence of clinically relevant central nervous system (CNS) pathology unrelated to CNS leukemia. * Presence of CNS-3 disease or CNS-2 disease with neurological changes at screening. * Presence of active or uncontrolled fungal, bacterial, viral, or other infection requiring systemic antimicrobials for management. * Patients who had prior (\< 3 months before obe-cel infusion) stem cell transplant. * Prior CD19 targeted therapy other than blinatumomab. * Patients who have experienced Grade ≥ 3 neurotoxicity following blinatumomab.