Phase 1 Study of BAFF CAR-T Cells (LMY-920) for Treatment of Relapsed or Refractory Chronic Lymphocytic Leukemia / Small Lymphocytic Lymphoma

Inclusion Criteria: 1. Histologically confirmed chronic lymphocytic leukemia (including small lymphocytic lymphoma) * Relapsed after 2 or more lines of therapy, including a BTK inhibitor and a BCL2 inhibitor. 2. No evidence of CNS lymphoma. 3. Male or female ≥ 18 years of age. 4. ECOG Performance status ≤ 2 \[See Appendix 1\]. 5. Presence of Presence of active disease for participants with CLL and SLL and presence of measurable disease for participants with SLL. A. CLL/SLL (note that SLL participants must have both measurable disease and active disease): Active disease as defined by the International Workshop on Chronic Lymphocytic Leukemia (iwCLL), with at least one of the following criteria21: * Evidence of progressive marrow failure as manifested by the development of, or worsening of, anemia and/or thrombocytopenia. Cutoff levels of Hb \<10 g/dL or platelet counts \<100 × 109/L are generally regarded as indication for treatment. * Massive (i.e., ≥6 cm below the left costal margin) or progressive or symptomatic splenomegaly. * Massive nodes (i.e., ≥10 cm in longest diameter) or progressive or symptomatic lymphadenopathy. * Symptomatic or functional extranodal involvement (e.g., skin, kidney, lung, spine, etc.). * Disease-related symptoms as defined by any of the following: * Unintentional weight loss ≥10% within the previous 6 months. * Significant fatigue (ie, ECOG performance scale 2 or worse; cannot work or unable to perform usual activities). * Fevers ≥100.5°F or 38.0°C for 2 or more weeks without evidence of infection. * Night sweats for ≥1 month without evidence of infection. B. Measurable disease for participants with SLL: At least one measurable lesion according to Lugano Revised Response Criteria for Malignant Lymphoma. 6. \>2 weeks since prior radiation therapy or 5 half-lives for systemic therapy at the time of leukapheresis, whichever is shorter (Note: Obinutuzumab pre-treatment of CLL/SLL participants must start at the latest 14 days prior to apheresis). 7. Total bilirubin ≤ 1.5 X upper institutional limit of normal (except in participants with Gilbert's syndrome, active hemolysis or disease involvement of the liver). 8. AST (SGOT)/ALT ≤ 2.5 X institutional upper limit of normal. 9. Calculated creatinine clearance ≥ 30ml/min. 10. Cardiac ejection fraction of ≥50% 11. Adequate pulmonary function as defined as pulse oximetry ≥ 92% on room air. 12. Participants (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document. 13. 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 BAFF CAR-T cell infusion. A woman is considered to be of childbearing potential if she is postmenarcheal, 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 participant. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. 14. 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 BAFF 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 BAFF 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 participant. Periodic abstinence (e.g., calendar, ovulation, symptothermal, or postovulation methods) and withdrawal are not acceptable methods of contraception. Exclusion Criteria: The presence of any of the following will exclude a participant from study enrollment: 1. ASCT within 6 weeks of informed consent. 2. History of allogeneic hematopoietic stem cell transplantation. 3. Active graft-versus-host disease. 4. Active central nervous system or meningeal involvement by lymphoma or leukemia. Participants with untreated brain metastases/CNS disease will be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. participants with a history of CNS or meningeal involvement must be in a documented remission by CSF evaluation and contrast-enhanced MRI imaging for at least 90 days prior to registration. 5. Active malignancy, other than non-melanoma skin cancer or carcinoma in situ (e.g., cervix, bladder, breast). 6. Known active additional malignancies which require systemic treatment (non-immediately morbid malignancies receiving only low-toxicity regimens such as hormone suppression for prostate or breast cancer may be allowed at the judgment of the investigator). 7. Less than 28 days elapsed between prior treatment with investigational agent(s) and the day of lymphocyte collection. 8. New York Heart Association class IV congestive heart failure. 9. Cardiovascular disorders including unstable angina pectoris, clinically significant cardiac arrhythmias, myocardial infarction or stroke (including transient ischemic attack, or other ischemic event) within 6 months prior to registration. 10. Active infection requiring intravenous systemic treatment. 11. HIV seropositivity. 12. Pregnant or breastfeeding women are excluded from this study because LMY-920 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 LMY-920, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study. 13. Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy. 14. Serologic status reflecting active hepatitis B or C infection. Participants 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 participants will be excluded.) 15. Participants with history of active and clinically relevant CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease. 16. Participants 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. 17. History of autoimmune disease (i.e., rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medications (other than low dose steroids) within 6 months. Pre-infusion Safety Check * Participants will undergo a pre-lymphodepletion safety check in the 48h preceding lymphodepletion with Fludarabine and Cyclophosphamide. The objective of these criteria is to avoid infusion in participants with acutely heightened risk of toxicity. * Participants must continue to meet eligibility criteria prior to initiation of lymphodepletive chemotherapy, with exception of the absolute lymphocyte count. This eligibility re-check will be done up to 48 hours prior to initiation of lymphodepletion. The following findings at the pre-lymphodepletion safety check will require a delay in chemotherapy administration until resolved: * Symptoms, signs or laboratory markers of active infection or systemic inflammatory response. * Symptoms, signs or laboratory markers of an uncontrolled medical condition, including but not limited to decompensation of cardiac or pulmonary conditions. These changes exclude symptoms, signs or laboratory markers of disease progression, as long eligibility criteria are met. If the condition that leads to failure to meet eligibility criteria is considered irreversible by the principal investigator, participant participation in the study will be discontinued. Participants will undergo a pre-infusion safety check on day -3 or 0. The objective of these criteria is to avoid infusion in participant with acutely heightened risk of toxicity. Participants must meet the following organ function criteria prior to LMY-920 cell infusion: * Total bilirubin ≤ 2 times the institutional upper limit of normal unless bilirubin rise is due to Gilbert's syndrome (maximum 2 times normal) or of non - hepatic origin. * AST (SGOT) and ALT (SGPT) ≤ 4 X institutional upper limit of normal * Serum Creatinine ≤ 2 X the institutional upper limit of normal * Participants must have adequate pulmonary function as defined as pulse oximetry ≥ 92% on room air. * Absence of clinical signs, symptoms, or laboratory markers of cardiac dysfunction. The following findings at the pre - infusion safety check will require a delay in the infusion until resolved: * Use of corticosteroids within 2 days prior to day 0 infusion, with the exception of agents used for prevention of emesis during lymphodepletive chemotherapy. * Neurologic symptoms suggestive of an active central nervous system condition. * Signs or laboratory markers of active infection or systemic inflammatory response. Participants presenting any of the following findings will NOT receive a LMY- 920 infusion: * Signs or laboratory markers of active infection or systemic inflammatory response. * Participants with fever over 38.2 degrees Celsius (detected in 2 separate measurements separated by at least 15 minutes) * Delay and re-conditioning (if delay is longer than 48 hours) can be considered in participants who have resolution of their symptoms.