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

This treatment uses T cells already present in the participant's body that have been modified outside of the body by a lentivirus and then returned by an infusion to target the cancer. Lentivirus is a family of viruses that can be used by scientists to alter cells. The specific type of cells that will be used is called UF-KURE19 chimeric antigen receptor T cells (CAR-T cells). The CAR-T cells that will be reinfused into the body are modified using a lentivirus that is no longer active. The investigators are evaluating UF-KURE19 because it uses a process that is shorter than other approved CAR-T cells. While the shorter manufacture time can be an advantage, the safety of this approach has not been demonstrated.