Anti-CD19 CAR T Cells in Pediatric Patients Affected by Relapsed/Refractory CD19+ ALL and NHL

Inclusion Criteria: 1. Male and female subjects with CD19 expressing B-cell acute lymphoblastic leukemia (ALL) or Non-Hodgkin Lymphoma (NHL) with BM involvement and one of the following: i. Patients in 2nd or subsequent relapse, after at least one standard frontline chemotherapy and one salvage regimen, with BM involvement ii. Relapse after allogeneic HSCT, if at least 100 days post-transplant, if there is no evidence of active GVHD and if the patient is no longer taking immunosuppressive agents for at least 30 days prior to enrollment iii. MRD \> 0.1% after either reinduction therapy or any course of consolidation for relapsed ALL 2. Measurable or evaluable disease at the time of enrollment, which may include any evidence of disease, including MRD detected by flow cytometry, cytogenetics, or polymerase chain reaction (PCR) analysis. 3. Age: 6 months - 25 years. 4. Voluntary informed consent is given. For subjects \< 18 year-old their legal guardian must give informed consent. Pediatric subjects will be included in age-appropriate discussion and verbal assent will be obtained for those greater than or equal to 12 years of age, when appropriate. 5. Clinical performance status: Patients \> 16 years of age: Karnofsky greater than or equal to 60%; Patients \< 16 years of age: Lansky scale greater than or equal to 60%. 6. Patients of child-bearing or child-fathering potential must be willing to practice birth control from the time of enrollment on this study and for four months after receiving the preparative regimen. 7. Females of child-bearing potential must have a negative pregnancy test because of the potentially dangerous effects on the fetus. Exclusion Criteria: 1. Pregnant or lactating women 2. Severe, uncontrolled active intercurrent infections 3. HIV, or active HCV and/or HBV infection 4. Life-expectancy \< 6 weeks 5. Hepatic function: Inadequate liver function defined as total bilirubin \> 4x upper limit of normal (ULN) or transaminase (ALT and AST) \> 6 x ULN 6. Renal function: serum creatinine \> 3x ULN for age. 7. Blood oxygen saturation \< 90%. 8. Cardiac function: Left ventricular ejection fraction lower than 45% by ECHO. 9. Congestive heart failure, cardiac arrhythmia, psychiatric illness, or social situations that would limit compliance with study requirements or in the opinion of the PI would pose an unacceptable risk to the subject. 10. BM blasts \> 50% pre-infusion. 11. Hyperleukocytosis (greater than or equal to 20,000 blasts/microliter) or rapidly progressive disease that in the evaluation of the investigator would compromise ability to complete study therapy 12. Active CNS disease as documented by the presence of blasts in the CSF or by MRI. This criterion could be revised once that, after the phase I portion of the study, absence of life-threatening (i.e. grade IV) neurological toxicity will be documented. 13. Presence of active, grade 2-4 acute or extensive chronic GvHD 14. Recurrent or refractory ALL with testicular involvement 15. Concurrent or recent prior therapies, before infusion: i. Systemic steroids (at a dose \> 2 mg/kg prednisone) in the 2 weeks before infusion. Recent or current use of inhaled/topical/non-absorbable steroids is not exclusionary. ii. Systemic chemotherapy in the 2 weeks preceding infusion. iii. Anti-thymocyte globulin (ATG) or Alemtuzumab (Campath®) in the 4 weeks preceding infusion. iv. Immunosuppressive agents in the 2 weeks preceding infusion. v. Radiation therapy must have been completed at least 3 weeks prior to enrollment. vi. Other anti-neoplastic investigational agents currently administered or within 30 days prior to infusion (i.e. start of protocol therapy); vii. Exceptions: 1. There is no time restriction with respect to prior intrathecal chemotherapy, provided that there is complete recovery from any acute toxic effects of such; 2. Patients who relapse while receiving standard ALL maintenance chemotherapy will not be required to have a waiting period before entry onto this study provided that they meet all other eligibility criteria; 3. Subjects receiving steroid therapy at physiologic replacement doses only are allowed provided that there has been no increase in dose for at least 2 weeks prior to starting apheresis; 16. Patient-derived CD19-CART01 production failure