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

Eligible Diseases: Relapsed or refractory pediatric B-Cell ALL as defined by at least one of the following criteria: * Second or greater relapse OR * Any relapse after allogeneic SCT OR * Not achieving a CR after 2 cycles of standard chemotherapy regimen (including persistent MRD positive disease) OR * Not achieving a CR after 1 cycle of standard chemotherapy for relapsed leukemia (including persistent MRD positive disease) OR * Patients with Philadelphia chromosome positive (Ph+) ALL who are intolerant or have failed 3 lines of tyrosine kinase inhibitor (TKI) therapy, or if TKI therapy is contraindicated OR * Patients who meet accepted indications for allogeneic HSCT for pediatric ALL but are deemed unfit for HSCT by their treating physician are eligible for this study. This includes high risk patients in first relapse. Patients with relapsed or refractory pediatric B cell non-Hodgkin's Lymphoma as defined by: * Refractory to second-line or later lines of standard chemotherapy OR * Patients with residual disease after primary therapy and not eligible for autologous SCT OR * Any relapse after previous allogeneic or autologous SCT OR * Beyond 1st CR with relapsed or persistent disease and not eligible or appropriate for conventional allogeneic or autologous SCT Note: patients with a history of blinatumomab therapy are eligible for this study. Inclusion Criteria: * For relapsed patients, CD19 tumor expression demonstrated in bone marrow or peripheral blood by flow cytome…