A Phase 1, Multicenter, Open-label Study of UB-VV111 in Combination With Rapamycin in Relapsed/Refractory (R/R) CD19+ B-cell Malignancies

Inclusion Criteria: 1. 18 years or older 2. Provides voluntary written informed consent 3. Relapsed or refractory large B-cell lymphoma (LBCL) or chronic lymphocytic leukemia (CLL) 4. Measurable disease according to Lugano 2014 criteria (LBCL) or iwCLL 2018 (CLL). 5. No serious concomitant diseases or active/uncontrolled infections 6. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 7. Adequate organ function 8. Patients who have previously received CD19-directed therapy must have biopsy confirming CD19 expression following completion of prior CD19-directed therapy. Exclusion Criteria: 1. Women who are pregnant or breastfeeding 2. Current isolated central nervous system (CNS) involvement 3. Prior allogeneic bone marrow transplant, gene therapy, or adoptive cell transfer (exceptions include tumor-infiltrating lymphocytes and CAR T cells) 4. History of or active human immunodeficiency virus (HIV) 5. Active hepatitis B or C 6. Systemic immunodeficiency diseases, except for well-controlled Type I diabetes or thyroid disease 7. Ongoing CNS disease that would preclude neurologic assessment 8. Uncontrolled angina or other acute heart disease 9. Currently receiving treatment in another interventional clinical trial.