CD45RA-depleted CD19-CAR T Cell Consolidation After TCRαβ+/CD19 B Cell-depleted Haploidentical Hematopoietic Cell Transplantation for Relapsed/Refractory CD19+ ALL and Lymphoma

Inclusion Criteria: Recipient * Age less than or equal to 21 years * High risk hematologic malignancy where allogeneic transplantation is the current standard of care. This includes (but is not limited to): * High risk CD19+ B cell ALL in CR1 or CR2 * Any CD19+ B-cell ALL in CR3 or subsequent * If prior CNS leukemia, it must be treated and in CNS CR * Left ventricular ejection fraction \> 40%, or shortening fraction ≥ 25% * Creatinine clearance (CrCl) or glomerular filtration rate (GFR) ≥ 50 ml/min/1.73m2 * Forced vital capacity (FVC) ≥ 50% of predicted value; or pulse oximetry ≥ 92% on room air if patient is unable to perform pulmonary function testing * Karnofsky or Lansky (age dependent) performance score ≥ 50 (See APPENDIX A) * Bilirubin ≤ 3 times the upper limit of normal for age * Alanine aminotransferase (ALT) or Aspartate aminotransferase (AST) ≤ 5 times the upper limit of normal for age Donor * At least single haplotype matched (≥ 4 of 8) family member * At least 18 years of age * HIV negative * If sexually active, agreement to use birth control until 2 weeks after completion of the mobilization and apheresis procedure * Regarding donation eligibility, is identified as either: * Completed the process of donor eligibility determination as outlined in 21 CFR 1271 and agency guidance; OR * Does not meet 21 CFR 1271 eligibility requirements, but has a declaration of urgent medical need completed by the principal investigator or physician sub-investigator per 21 CFR 1271 Exclusion Criteria: Recipient * Has a suitable HLA-identical sibling or suitable 12/12 (HLA-A, B, C, DRB1, DQB1, and DPB1) HLA-matched unrelated donor available in an appropriate time frame * Any other active malignancy other than the one for which this HCT is indicated * Received a prior allogeneic HCT at any time * Pregnant, if female is of childbearing potential, negative test must be confirmed by serum or urine pregnancy test within 14 days prior to enrollment * If sexually active, agreement to use birth control until 6 months after T cell infusion * Breast feeding * Any severe current uncontrolled bacterial, fungal or viral infection Donor * Pregnant, negative test must be confirmed by serum or urine pregnancy test within 14 days prior to enrollment if female * If female, breast feeding