This is a Phase I, open-label dose finding study to assess the safety and feasibility, pharmacokinetics, and preliminary efficacy of TmCD19-IL18 CAR T cells in patients with CD19+ cancers. This study will take place in two parts: a Dose-Finding Phase to determine the maximum tolerate dose (MTD), followed by a Dose Expansion Phase. In the Dose-Finding Phase, dose levels will be evaluated using a 3+3 dose escalation design to determine the MTD. Cumulative safety experience and manufacturing feasibility data from the Dose-Finding Phase will then be used to identify the dose level that can be progressed into the Dose Expansion Phase.

1. Signed informed consent form

2. Documentation of CD19 expression on malignant cells by flow cytometry/IHC from a CLIA certified laboratory.

   a. Cohort A (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.

3. Patients with relapsed disease after prior allogeneic SCT must meet the following criteria:

   1. Have no active GVHD and require no immunosuppression
   2. Are more than 6 months from transplant at the time of physician-investigator confirmation of eligibility

4. Adequate organ function defined as:

   1. Estimated creatinine clearance > 35 mL/min and not on dialysis
   2. ALT/AST ≤ 3x upper limit of normal range
   3. Direct bilirubin ≤ 2.0 mg/dl, unless the subject has Gilbert's syndrome (≤3.0 mg/dl)
   4. Must have a minimum level of pulmonary reserve defined as ≤ Grade 1 dyspnea and pulse oxygen > 92% on room air
   5. Left Ventricle Ejection Fraction (LVEF) ≥ 40% confirmed by ECHO

5. Evidence of active disease within 12 weeks of physician-investigator confirmation of eligibility.

6. Male or female age ≥ 18 years.

7. ECOG Performance Status that is either 0 or 1.

8. Disease-specific criteria:

   a. Cohort A (NHL): i. Patients with any of the following diagnoses: Diffuse Large B-cell Lymphoma not otherwise specified (DLBCL NOS), germinal center or activated B-cell types; Primary Cutaneous DLBCL; Primary Mediastinal (thymic) Large B-cell Lymphoma; ALK+ Anaplastic Large B-cell Lymphoma; High-Grade B-cell Lymphoma with MYC and BCL2 and/or BCL6 rearrangements (i.e., "Double or Triple Hit"); High-grade B-cell Lymphoma, NOS; T-cell Rich B-cell Lymphoma; Transformed Follicular Lymphoma; or any aggressive B-cell lymphoma arising from indolent lymphoma.

1. Patients must have either relapsed after, or be ineligible for, prior CAR T cell therapy, and meet one of the following criteria:

1. Relapsed/refractory disease after at least 2 prior lines of appropriate therapy; OR
2. Relapsed/refractory disease after autologous SCT; OR
3. Relapsed/refractory disease after allogeneic SCT.

ii. Follicular lymphoma

1. Patients must have either relapsed after, or be ineligible for, prior commercial CAR T cell therapy; AND
2. Received at least 2 prior lines of appropriate therapy (not including single agent monoclonal antibody therapy) and progressed within 2 years after second or higher line of therapy.

iii. Mantle cell lymphoma

1. Patients must have either failed standard of care CAR T cell therapy (e.g., Tecartus™, etc.) or other investigational CAR T cell product, OR be ineligible for standard of care Tecartus™; and

2. Patients must also meet one of the following criteria:

   1. 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; OR
   2. Relapsed/refractory disease after prior autologous SCT; OR
   3. Relapsed/refractory disease after prior allogeneic SCT. iv. Marginal Zone Lymphoma

1. Patients must have received at least 2 prior lines of appropriate therapy which includes a BTK inhibitor (not including single agent monoclonal antibody therapy).

Exclusion Criteria:

1. Active hepatitis B, active hepatitis C, or other active, uncontrolled infection.

2. Class III/IV cardiovascular disability according to the New York Heart Association Classification.

3. Clinically apparent arrhythmia or arrhythmias that are not stable on medical management within two weeks of physician-investigator confirmation of eligibility.

4. Active acute or chronic GVHD requiring systemic therapy.

5. Dependence on systemic steroids or immunosuppressant medications. For additional details regarding use of steroid and immunosuppressant medications.

6. Receipt of prior huCART19-IL18 therapy.

7. CNS disease as defined by disease-cohort as follows:

   a. Cohort A: Active CNS disease. Note: Patients with a history of CNS involvement that was successfully treated are eligible. A CNS evaluation is only required for eligibility if a subject is experiencing signs/symptoms of CNS involvement.

8. Pregnant or nursing (lactating) patients. Participants of reproductive potential must agree to use acceptable birth control methods.

9. 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.

10. Active autoimmune disease requiring systemic immunosuppressive treatment equivalent to ≥ 10mg of prednisone. Patients with autoimmune neurologic diseases (such as MS) will be excluded.