Autologous HuCART19 T Cells Manufactured Using the CliniMACS Prodigy Platform for Pediatric B-ALL (huCART19 Prodigy)

Inclusion Criteria: 1. Signed Informed Informed Consent 2. Subjects with documented CD19+ ALL or Lly: a. Cohort A: Subjects with relapsed or refractory ALL or Lly who have not previously received CAR T-cell Therapy: i. 2nd or greater relapse (marrow or extramedullary) OR ii. Any relapse after allogeneic HSCT and ≥4 months from HSCT at enrollment OR iii. Refractory disease defined as having not achieved an MRD-negative (by multiparameter flow cytometry) or CSF-negative CR after ≥2 chemotherapy regimens/cycles of frontline therapy, or 1 cycle of reinduction therapy for subjects in first relapse OR iv. Newly diagnosed NCI high-risk B-ALL with induction failure, defined as a M3 bone marrow (≥25%) blasts at the end of induction chemotherapy OR v. First bone marrow relapse of B-ALL at \<36 months after initial diagnosis OR vi. First or greater CNS relapse of B-ALL vii. Ineligible for allogeneic HSCT because of at least one of the following: 1\. Comorbid disease 2. Other contraindications to HSCT conditioning regimen 3. Lack of suitable donor 4. Prior HSCT 5. Declines HSCT as the therapeutic option after documented discussion, with expected outcomes, and the role of HSCT with a BMT physician not a part of the study team. b. Cohort B: Subjects with poor response to prior B cell directed engineered cell therapy, defined as any one of the following: i. Partial response or no response to prior cell therapy ii. CD19+ relapse after prior cell therapy, defined as bone marrow blasts \> 0.01% by multiparameter flow cytometry or evidence of extramedullary disease iii. Demonstrated early (≤6 months from infusion) B cell recovery suggesting loss of engineered cells 3\. Subjects with prior or current history of CNS3 disease will be eligible if Central Nervous System (CNS) disease is responsive to therapy. 4\. Documentation of CD19 tumor expression in bone marrow, peripheral blood, cerebrospinal fluid (CSF), or tumor tissue by flow cytometry. If the subject has received CD19-directed therapy, flow cytometry should be obtained after this therapy to demonstrate CD19 expression. 5\. Age 0-29 years 6\. Adequate organ function. a. Serum creatinine based on age/gender b. Adequate liver function: i. ALT within 5x ULN in the absence of ALL infiltration of the liver ii. Bilirubin ≤3x the upper limit of normal iii. ALT and/or bilirubin results that exceed this range are acceptable if, in the opinion of the physician-investigator (or as confirmed by liver biopsy), the abnormalities are directly related to ALL infiltration of the liver. c. Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea and \< Grade 3 hypoxia; DLCO ≥ 40% (corrected for anemia if necessary) if PFTs are clinically appropriate as determined by the investigator. d. Left Ventricular Shortening Fraction (LVSF) ≥28% or Ejection Fraction (LVEF) ≥45% confirmed by echocardiogram or another scan. In cases where quantitative assessment of LVSF/LVEF is not possible, a statement by the cardiologist that the ECHO shows qualitatively normal ventricular function will suffice. 7\. Adequate performance status defined as Lanksy or Karnofsky performance score ≥50 8\. Subjects of reproductive potential must agree to use acceptable birth control methods. Exclusion Criteria: 1. Active hepatitis B or active hepatitis C 2. HIV infection 3. Active acute or chronic graft-versus-host disease (GVHD) requiring systemic therapy. 4. Concurrent use of systemic steroids or immunosuppression at the time of cell infusion or cell collection, or a condition, in the treating physician's opinion, that is likely to require steroid therapy or immunosuppression during collection or after infusion. Steroids for disease treatment at times other than cell collection or at the time of infusion are permitted. Use of physiologic replacement hydrocortisone or inhaled steroids is permitted as well. 5. CNS disease that is progressive on therapy, or with CNS parenchymal lesions that might increase the risk of CNS toxicity. 6. Subjects who are pregnant or nursing. 7. Uncontrolled active infection. 8. History of seizure disorder that requires ongoing anti-epileptic therapy. 9. If the subject has received previous CAR T cell therapies, history of grade 3 or higher ICANS following administration of a CAR T cell product.