CD19 Chimeric Antigen Receptor (CAR) T Cells for Adults With Recurrent or Refractory B Cell Malignancies

Inclusion Criteria: * Participants must be greater than or equal to 18 years of age. * Participants must have Eastern cooperative oncology group (ECOG) performance status of 0 or 1, or Karnofsky greater than or equal to 80% * Participants must have been diagnosed with histologically confirmed aggressive B cell NHL that is refractory / recurrent. * Participants must have been diagnosed with histologically confirmed B-ALL that is refractory / recurrent. * All subjects must have evaluable or measurable disease; subjects with lymphoma must have evaluable or measurable disease according to the revised IWG Response Criteria for Malignant Lymphoma. Lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. ALL patients must have at least 5% blasts in the bone marrow * Adequate performance status; adequate organ and marrow function as defined by (supportive care is allowed per institutional standards, i.e. filgrastim, transfusion): * ANC ≥ 750/uL\* * Platelet count ≥ 50,000/uL\* * Absolute lymphocyte count ≥ 150/uL\* * Adequate renal, hepatic, pulmonary and cardiac function defined as: * SaO2 ≥ 92% on room air * Creatinine ≤ 2 mg/dL or Creatinine Clearance ≥ 60 mL/min (as estimated by Cockcroft Gault) * Total bilirubin ≤ 1.5 mg/dL (except in subjects with Gilbert's disease) (Elevations related to leukemia or lymphoma involvement of the liver will not disqualify a subject) * Serum ALT/AST ≤3x ULN or ≤5X if there is hepatic involvement due to malignancy * Cardiac ejection fraction (LVEF) ≥ 45%) * Subjects with ALL or B-NHL with CNS1, or CNS1a, 2b, 2c are eligible only in the absence of neurologic symptoms suggestive of CNS disease involvement such as cranial nerve palsy. * If patients previously had CNS disease and are disease free after treatment with no clinical concerns for recurrent disease they are eligible for enrollment. * Subjects with history of allogeneic SCT must be at least 100 days from SCT, have no evidence of Graft versus Host Disease (GvHD), and no longer taking immunosuppressive agents for at least 30 days prior to enrollment. However, patients with grade 1 skin GVHD or low grade cGHVD \<3 who are not requiring systemic therapy are eligible. * Females of child bearing potential and males of child fathering potential must be willing to practice birth control during and for 4 months post therapy. * Females of child bearing potential must have negative pregnancy test. * Must meet wash out period since prior therapies. * At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy at the time the subject is planned for leukapheresis, except for systemic inhibitory/stimulatory immune checkpoint therapy, which requires 5 half-lives * Must have recovered from acute side effects from prior therapy to meet eligibility. * If had prior CAR therapy, 30 days must have elapsed prior to apheresis; may not have evidence of persistence of CAR T cells in blood samples (circulating levels of genetically modified cells of ≥ 5% by flow cytometry) * No active HIV or active HBV/HCV infection. Patients with history of HBV or HCV who are PCR negative after appropriate therapy are eligible. Patients may not have any other uncontrolled, symptomatic, intercurrent illness. * No history of severe, immediate hypersensitivity reaction attributed to compounds of similar chemical or biologic composition to any agents used in study. * No active CNS disorder, or history of MI, cardiac angioplasty or stenting, unstable angina or other clinically significant cardiac disease with 12 months of enrollment, or have cardiac atrial or ventricular lymphoma involvement. * Not receiving anticoagulation therapy * Not have primary immunodeficiency or history of autoimmune disease (e.g. Crohns, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years Exclusion Criteria: * Participants must not have an active bacterial, viral, fungal or other infection. * Participants must not have a history of HIV or current hepatitis B or hepatitis C virus * Participants must not have a history of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment, or have cardiac atrial or cardiac ventricular lymphoma involvement. * No history of severe, immediate hypersensitivity reaction attributed to compounds of similar chemical or biologic composition to any agents used in study. * No active CNS disorder, or history of MI, cardiac angioplasty or stenting, unstable angina or other clinically significant cardiac disease with 12 months of enrollment, or have cardiac atrial or ventricular lymphoma involvement. * Not receiving anticoagulation therapy * Not have primary immunodeficiency or history of autoimmune disease (e.g. Crohns, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years * History of malignancy other than non-melanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, and breast) unless disease free for at least 1 year. Patients who are on adjuvant therapy with no evidence of active disease are deemed eligible for the trial