Safety and Feasibility of CD19 CAR T Cells Using CliniMACS Prodigy for Relapsed/Refractory CD19 Positive ALL and NHL

PRIMARY OBJECTIVE: * To examine the feasibility of manufacture and administration of autologous CD19 CAR T cells at a minimum target dose of 0.3 x 10\^6 to 1 x 10\^6 per kilogram for patients \<50 kg and a flat dose of 0.3 - 1 x 10\^8 for patients ≥50 kg using the Miltenyi CliniMACS Prodigy automated T Cell Transduction (TCT) process. * To evaluate the safety of administration of CD19 CAR T cells after lymphodepletion with fludarabine and cyclophosphamide. SECONDARY OBJECTIVE: • To estimate the efficacy of CD19 specific CAR-T cells in pediatric and young adult patients with relapsed/refractory CD19+ B-cell ALL and NHL. EXPLORATORY OBJECTIVE: • To evaluate the persistence of CD19 CAR T cells after infusion. The autologous lymphocytes are collected from the patient via apheresis. The apheresis product is then transported to the on-site GMP facility for manufacture of the CAR T cell product. Patients may be admitted to begin lymphodepleting chemotherapy during the CAR T cell manufacturing process. When the CAR T cell product is ready, the cells may be administered fresh or may be cryopreserved for use at a later date depending on the patient's clinical status. All patients will be admitted to the hospital to undergo a Fludarabine/Cyclophosphamide based leukoreduction conditioning regimen to be completed 2-14 days prior to CAR T cell infusion. Patients will be admitted for a minimum of 7 days after the CAR T infusion to monitor for toxicity including cytokine release syndrome, neurologic toxicity, and tumor lysis syndrome. Lymphodepleting chemotherapy: * Fludarabine 30 mg/m2/day IV x 4 days * Cyclophosphamide 500 mg/m2/day IV x 2 days CD19 CAR T cell dose: * 0.3 x 10\^6 to 1 x 10\^6 per kilogram for patients \<50 kg * Flat dose of 0.3 - 1 x 10\^8 for patients ≥50 kg