BAFF CAR-T Cells (LMY-920) for Treatment of Relapsed or Refractory Non-Hodgkin Lymphoma and Multiple Myeloma

Inclusion Criteria: 1. Histologically confirmed: a. B cell NHL (Including but not limited to diffuse large B cell lymphoma, follicular lymphoma, mantle cell lymphoma, marginal zone lymphoma, chronic lymphocytic leukemia and small lymphocytic lymphoma) i. Relapsed after 2 or more lines of therapy, or ii. Have disease refractory to prior chemotherapy (defined as progressive disease or stable disease lasting ≤ 6 months, as best response to most recent chemotherapy regimen; or disease progression, or recurrence ≤ 12 months after prior autologous stem cell transplantation (ASCT). iii. At least one measurable lesion according to Lugano Revised Response Criteria for Malignant Lymphoma. OR b. MM i. Relapsed or refractory after 3 or more lines of therapy including an immunomodulatory agent, a proteasome inhibitor and an anti-CD38 antibody. ii. Measurable disease per IMWG uniform response criteria 2. No evidence of CNS lymphoma. 3. Participant is ≥ 18 years of age. 4. ECOG Performance status ≤ 2. 5. \> 2 weeks since prior radiation therapy or systemic therapy at the time of leukapheresis. Patients with mantle cell lymphoma that can only remain stable with continuation of prior BTK inhibitor may continue these agents up to 48 hours prior to apheresis. 6. Adequate organ function as defined by: 1. Total bilirubin ≤ 1.5× institutional upper limit of normal (except in patients with Gilbert's syndrome, active hemolysis or disease involvement of the liver.) 2. AST (SGOT)/ALT ≤ 2.5 × institutional upper limit of normal. 3. Calculated creatinine clearance ≥ 30ml/min. 4. Cardiac ejection fraction of ≥ 50% 5. Adequate pulmonary function as defined as pulse oximetry ≥ 92% on room air. 7. Subjects (or legal guardians) must have the ability to understand and the willingness to sign a written informed consent document. 8. 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 6 months after the BAFF CAR-T cell infusion. 9. For men: agreement to remain abstinent (refrain from heterosexual intercourse) or use contraceptive measures with a failure rate of \< 1% per year during the treatment period , and agreement to refrain from donating spermfor at least 6 months after the BAFF CAR-T cell infusion. Exclusion Criteria: 1. ASCT within 6 weeks prior to informed consent. 2. History of allogeneic transplantation. 3. Active graft-versus-host disease. 4. Active central nervous system or meningeal involvement by lymphoma or leukemia. Subjects 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. Patients 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 enrollment. 5. 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.) 6. Less than 28 days elapsed between prior treatment with investigational agent(s) and the day of lymphocyte collection. 7. Cardiovascular disorders including symptomatic congestive heart failure, unstable angina pectoris, clinically significant cardiac arrhythmias, myocardial infarction or stroke (including transient ischemic attack, or other ischemic event). 8. Active infection requiring intravenous systemic treatment. 9. HIV seropositivity. 10. Pregnant or breastfeeding women are excluded from this study. 11. Evidence of myelodysplasia or cytogenetic abnormality indicative of myelodysplasia on any bone marrow biopsy prior to initiation of therapy. 12. 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.) 13. Patients 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. 14. Subjects with uncontrolled intercurrent illness or psychiatric illness/social situations that would limit compliance with study requirements. 15. History of autoimmune disease (i.e., rheumatoid arthritis, systemic lupus erythematosus) with requirement of immunosuppressive medications (other than low dose steroids) within 2 months.