A Phase II Study to Evaluate the Efficacy of UF-KURE19 Cells in Patients With Relapsed or Refractory B Cell Non-Hodgkin Lymphomas

Inclusion Criteria: 1. Male or female patients aged 18 years or older. 2. Participants must have histologically confirmed, CD19 positive (by IHC or flow cytometry) NHL at the most recent biopsy. If a previous CD19 targeting therapy was utilized, a biopsy should be available after this therapy demonstrating sustained CD19 expression. 3. Subjects in cohort 1 (LBCL) must meet the following inclusion criteria: a. Subjects must fit one of the following diagnoses: i. Diffuse large B-cell lymphoma (DLBCL) not otherwise specified (including DLBCL arising from indolent lymphoma) ii. High-grade B-cell lymphoma iii. Primary mediastinal large B-cell lymphoma iv. Follicular lymphoma grade 3B b. LBCL disease status must consist of one of the following: i. Relapsed after 2 or more lines of chemoimmunotherapy OR ii. Disease that is refractory to first line chemoimmunotherapy or relapses within 12 months of completion of initial chemoimmunotherapy OR iii. Relapsed disease that is ineligible to receive hematopoietic stem cell transplantation due to comorbidities or age or patient preference 4. Subjects in cohort 2 (FL) must meet the following inclusion criteria: a. Subjects must fit one of the following diagnoses: i. Follicular lymphoma ii. Marginal zone lymphoma b. Disease status must have relapsed after 2 or more lines of therapy 5. ECOG Performance status ≤ 2. 6. Participants must exhibit measurable disease with at least one FDG avid lesion at enrollment per Lugano Criteria 7. Minimum of 2 weeks since prior radiation therapy or systemic therapy to treat malignancy at the time of leukapheresis. 8. Total bilirubin ≤ 1.5X institutional upper limit of normal. 9. AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit of normal. 10. Calculated creatinine clearance ≥ 30mL/min estimated by the Cockcroft - Gault formula. 11. Cardiac ejection fraction of ≥ 45%. 12. Adequate pulmonary function, defined as ≤ Grade 1 dyspnea (unless considered secondary to lymphoma) and oxygen saturation (SaO2) ≥ 90% on room air. 13. Subjects (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document. 14. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 90 days after the UF-KURE19 CAR-T cell infusion. A woman is considered to be of childbearing potential if she is post menarcheal, has not reached a postmenopausal state (\< 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. 15. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below: With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after the UF-KURE19 CAR-T cell infusion. Men must refrain from donating sperm during this same period. With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the UF-KURE19 CAR-T cell infusion to avoid potential embryonal or fetal exposure. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. 16. Inclusion of Women and Minorities: Men, women and members of all races and ethnic groups are eligible for this trial. Exclusion Criteria: * Inclusion Criteria 1. Male or female patients aged 18 years or older. 2. Participants must have histologically confirmed, CD19 positive (by IHC or flow cytometry) NHL at the most recent biopsy. If a previous CD19 targeting therapy was utilized, a biopsy should be available after this therapy demonstrating sustained CD19 expression. 3. Subjects in cohort 1 (LBCL) must meet the following inclusion criteria: a. Subjects must fit one of the following diagnoses: i. Diffuse large B-cell lymphoma (DLBCL) not otherwise specified (including DLBCL arising from indolent lymphoma) ii. High-grade B-cell lymphoma iii. Primary mediastinal large B-cell lymphoma iv. Follicular lymphoma grade 3B b. LBCL disease status must consist of one of the following: i. Relapsed after 2 or more lines of chemoimmunotherapy OR ii. Disease that is refractory to first line chemoimmunotherapy or relapses within 12 months of completion of initial chemoimmunotherapy OR iii. Relapsed disease that is ineligible to receive hematopoietic stem cell transplantation due to comorbidities or age or patient preference 4. Subjects in cohort 2 (FL) must meet the following inclusion criteria: a. Subjects must fit one of the following diagnoses: i. Follicular lymphoma ii. Marginal zone lymphoma b. Disease status must have relapsed after 2 or more lines of therapy 5. ECOG Performance status ≤ 2. 6. Participants must exhibit measurable disease with at least one FDG avid lesion at enrollment per Lugano Criteria 7. Minimum of 2 weeks since prior radiation therapy or systemic therapy to treat malignancy at the time of leukapheresis. 8. Total bilirubin ≤ 1.5X institutional upper limit of normal. 9. AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit of normal. 10. Calculated creatinine clearance ≥ 30mL/min estimated by the Cockcroft - Gault formula. 11. Cardiac ejection fraction of ≥ 45%. 12. Adequate pulmonary function, defined as ≤ Grade 1 dyspnea (unless considered secondary to lymphoma) and oxygen saturation (SaO2) ≥ 90% on room air. 13. Subjects (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document. 14. For women of childbearing potential: agreement to remain abstinent (refrain from heterosexual intercourse) or use a contraceptive method with a failure rate of \< 1% per year during the treatment period and for at least 90 days after the UF-KURE19 CAR-T cell infusion. A woman is considered to be of childbearing potential if she is post menarcheal, has not reached a postmenopausal state (\< 12 continuous months of amenorrhea with no identified cause other than menopause), and has not undergone surgical sterilization (removal of ovaries and/or uterus). Examples of contraceptive methods with a failure rate of \< 1% per year include bilateral tubal ligation, male sterilization, hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. 15. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures, and agreement to refrain from donating sperm, as defined below: With female partners of childbearing potential, men must remain abstinent or use a condom plus an additional contraceptive method that together result in a failure rate of \< 1% per year during the treatment period and for at least 6 months after the UF-KURE19 CAR-T cell infusion. Men must refrain from donating sperm during this same period. With pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 6 months after the UF-KURE19 CAR-T cell infusion to avoid potential embryonal or fetal exposure. The reliability of sexual abstinence should be evaluated in relation to the duration of the clinical trial and the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. 16. Inclusion of Women and Minorities: Men, women and members of all races and ethnic groups are eligible for this trial. Exclusion Criteria 1. Autologous stem cell transplant within 12 weeks of informed consent. 2. History of allogeneic hematopoietic stem cell transplantation. 3. Second active malignancy that is not another NHL, other than non-melanoma skin cancer, carcinoma in situ (e.g. cervix, bladder, breast), stage 1 uterine cancer, or localized prostate cancer. 4. Less than 28 days or 5 half-lives elapsed whichever is shorter between prior treatment with investigational agent(s) and leukapheresis. 5. New York Heart Association class III-IV congestive heart failure. 6. Cardiovascular disorders including unstable angina pectoris, clinically significant and uncontrolled cardiac arrhythmias, myocardial infarction or stroke (including transient ischemic attack, or other ischemic event) within 6 months prior to registration. 7. Confirmed active human immunodeficiency virus (HIV) infection. 8. Pregnant or breastfeeding women are excluded from this study because CAR-T cell therapy may be associated with the potential for teratogenic or abortifacient effects. Women of childbearing potential must have a negative serum pregnancy test. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with CAR-T cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study. 9. Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy. 10. Serologic status reflecting active hepatitis B or C infection. Patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment. (PCR positive patients will be excluded). 11. Patients with history of clinically relevant CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease. 12. Subjects with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, pulmonary abnormalities or psychiatric illness/social situations that would limit compliance with study requirements. 13. History of active autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of systemic immunosuppressive medications other than low dose steroids \[i.e. maximum of 15mg prednisone equivalent\] within the last 6 months. 14. History of leukemic phase lymphoma or presence of 1% or more circulating lymphoma cells at subject enrollment. 15. Previous treatment with a CD19 CAR-T product