Inclusion Criteria:  Signed informed consent form  Documentation of CD19 expression on malignant cells  a. ALL/CLL: At time of most recent relapse b. NHL: Within 6 months of physician-investigator confirmation of eligibility as long as there has been no intervening CD19 directed therapy since expression confirmed. Results outside of this window may be used, if there is no accessible tumor site and the subject did not receive intervening CD19 directed therapy since CD19 expression was confirmed.  Patients with relapsed disease after prior autologous or allogeneic SCT must meet the following criteria:  a. Have no active GVHD and require no immunosuppression b. Are more than 6 months from transplant at the time of physician-investigator confirmation of eligibility  Adequate organ function defined as:  Creatinine ≤ 1.6 mg/dl ALT/AST ≤ 3x upper limit of normal range Direct bilirubin ≤2.0 mg/dl, unless the subject has Gilbert's syndrome (≤3.0 mg/dl) Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea, pulse oxygen > 92% on room air, and DLCO ≥ 40% (corrected for anemia) Left Ventricle Ejection Fraction (LVEF) ≥ 40% confirmed by ECHO/MUGA Evidence of active disease. This could include circulating disease in the blood, disease in the bone marrow by standard morphology (or by MRD testing for ALL patients), or measurable disease per Lugano Criteria (NHL patients). Male or female age ≥ 18 years. ECOG Performance Status that is either 0 or 1. Subjects of reproductive potential must agree to use acceptable birth control methods.  Disease-specific criteria:  a. Cohort A i. Patients with relapsed or refractory B cell ALL which meets one of the following criteria:  Relapsed or refractory B cell ALL with 2nd or greater relapse or refractory to 1st salvage as defined by:  a. Recurrent disease in the blood or bone marrow identified morphologically, by immunohistochemistry or by Flow cytometry.  b. Patients with extramedullary relapse only (no bone marrow involvement) will be eligible if disease response can be assessed radiographically, OR  Refractory B cell ALL as defined by:  a. Failure to achieve remission (<5% bone marrow blasts) after 2 cycles of induction chemotherapy b. Patients that achieve morphologic remission but remain MRD+ after ≥2 cycles of induction chemotherapy, OR  Ph+ relapsed or refractory B cell ALL that is intolerant to or have failed a tyrosine kinase inhibitor therapy containing regimen.  ii. Patients with prior or current history of CNS3 disease* will be eligible only if CNS disease is responsive to therapy (at infusion, must meet criteria in Section 5.2) 1. *CNS disease definitions70:  a. CNS1 - no blasts seen on cytocentrifuge (CNS negative); b. CNS2 - total nucleated cell count <5x106/L, but blasts seen on cytocentrifuge; c. CNS3 - total nucleated cell count 5x106/L with blasts on cytocentrifuge and/or signs of CNS leukemia (i.e. cranial nerve palsy).  b. Cohort B (CLL) i. Patients must have relapsed/refractory disease after at least 2 prior lines of appropriate therapy, AND ii. Patients must have previously received, or be intolerant to an approved BTK inhibitor and venetoclax; unless a BTK inhibitor or venetoclax is contraindicated.  c. Cohort B (NHL)- With one of the following diagnoses: i. Diffuse Large B-cell Lymphoma  Patients with any of the following histologies:  Diffuse large B-cell lymphoma (DLBCL), NOS  i. Germinal center B-cell type ii. Activated B-cell type b. Primary cutaneous DLBCL, leg type c. Primary mediastinal (thymic) large B-cell lymphoma d. ALK+ large B-cell lymphoma e. High-grade B-cell lymphoma, with MYC and BCL2 and/or BCL6 rearrangements (i.e. "Double or Triple Hit") f. High-grade B-cell lymphoma, NOS  Patients must have relapsed after, or be ineligible for, prior CAR T cell therapy, and meet one of the following criteria:  Relapsed/refractory disease after at least 2 prior lines of appropriate therapy and are ineligible for autologous stem cell transplant or commercial CAR T cell therapy. Relapse/refractory disease after autologous SCT. Relapsed/refractory disease after allogeneic SCT. ii. Large cell transformation of CLL (Richter's transformation)  1. Patients must be primary refractory or received at least 1 prior line of treatment.  iii. Follicular lymphoma 1. Patients who have received at least 2 prior lines of appropriate therapy (not including single agent monoclonal antibody therapy), AND 2. Progressed within 2 years after second or higher line of therapy. iv. Mantle cell lymphoma  Patients must have either failed or be ineligible for standard of care Tecartus™ (brexucabtagene autoleucel) or other investigational CAR T cell product; and  Patients must also meet one of the following criteria:  Relapsed/refractory disease after at least 2 prior lines of appropriate therapy, including a BTK inhibitor. Single-agent monoclonal antibody therapy does not count towards prior lines of therapy. Relapsed/refractory disease after prior autologous SCT. Relapsed/refractory disease after prior allogeneic SCT..  Exclusion Criteria:  Active hepatitis B, active hepatitis C, or other active, uncontrolled infection. Class III/IV cardiovascular disability according to the New York Heart Association Classification. Clinically apparent arrhythmia or arrhythmias who are not stable on medical management within two weeks of physician-investigator confirmation of eligibility. Active acute or chronic GVHD requiring systemic therapy. Dependence on systemic steroids or immunosuppressant medications. For additional details regarding use of steroid and immunosuppressant medications. Receipt of immune checkpoint inhibitors within 4 months prior to physician-investigator confirmation of eligibility. CNS3 disease that is progressive on therapy, or with CNS parenchymal lesions. Pregnant or nursing (lactating) women. Patients with a known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system, and unrelated to their cancer or previous cancer treatment. Active autoimmune disease requiring systemic immunosuppressive treatment equivalent to ≥ 10mg of prednisone. Patients with autoimmune neurologic diseases (such as MS) will be excluded.