Evaluate the Safety of UF-KURE19 Cells in Non-Hodgkin Lymphomas

Phase 1 Cohort: Inclusion Criteria: * Male or female patients aged 18 years or older. * Participants must have histologically confirmed, CD19 positive (by IHC or flow cytometry) NHL that meets at least one of the following treatment indications. * Relapsed after 2 or more lines of chemotherapy, (or) * Refractory to chemotherapy, defined as: Progressive disease while receiving last chemotherapy, or Persistent disease after first line chemotherapy treatment with curative intent or stable disease lasting ≤6 months after last chemotherapy, or relapse within 6 months of last chemotherapy, or disease progression or relapse ≤12 months after prior autologous stem cell transplant, (or) * Relapsed disease that is ineligible to receive hematopoietic stem cell transplantation due to comorbidities or age or patient preference. * ECOG Performance status ≤ 2. * At least one measurable lesion according to Lugano Revised Response Criteria for Malignant Lymphoma. * Minimum of 2 weeks since prior radiation therapy or systemic therapy to treat malignancy at the time of leukapheresis. * Total bilirubin ≤ 1.5X institutional upper limit of normal. * AST (SGOT)/ALT (SGPT) ≤ 2.5 X institutional upper limit of normal. * Calculated creatinine clearance ≥ 30mL/min estimated by the Cockcroft - Gault formula. * Cardiac ejection fraction of ≥45%, and no more than trivial (or trace, minimal or mild) pericardial effusion, as determined by an echocardiogram. * Adequate pulmonary function, defined as …