• PRE-REGISTRATION: Age ≥ 18 years

• PRE-REGISTRATION: Confirmed diagnosis of 1 of the following relapsed or refractory B-cell hematologic malignancies: chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), follicular lymphoma (FL), mantle cell lymphoma (MCL), marginal zone lymphoma (MZL), or large B cell lymphoma (LBCL) including Richter's transformation from CLL/SLL

‣ For CD19+ B cell malignancies; relapsed or refractory disease is defined by one of the following histopathology:

• Biopsy proven SLL or flow cytometry proven CLL; relapsed or refractory disease is defined as:

∙ Demonstration of progressive or stable disease by positron emission tomography/computed tomography (PET/CT) or computed tomography (CT) criteria according to the international workshop on chronic lymphocytic leukemia (iwCLL) 2018 criteria

∙ Biopsy proven B-cell non-Hodgkin lymphoma (NHL) of any histopathology (including Richter Transformation of CLL); relapsed or refractory disease is defined as:

∙ Demonstration of progressive or stable disease by PET/CT or CT criteria as the best response to the most recent chemotherapy regimen according to the revised Lugano Response Criteria for Malignant Lymphoma

• PRE-REGISTRATION: Disease Specific prior lines of therapies below:

‣ For CLL/SLL, patients must have received ≥ two prior lines of therapy, and/or ≥ 6 months of second line prior BTK inhibition (e.g. ibrutinib or other such as acalabrutinib or zanubrutinib) and must have failed to respond to venetoclax or be intolerant. Exception: Patients in stable disease (SD) or partial response (PR) with a known ibrutinib resistance mutation (BTK or phospholipase Cγ2) may be included even if on ibrutinib therapy for less than 6 months

• These patients may or may not have received prior antibody directed against cluster of differentiation 20 (CD20).

⁃ For Follicular Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20.

• NOTE: Prior cluster of differentiation 19 (CD19) directed chimeric antigen receptor T-cell therapy (CART) must have a 100-day washout period.

⁃ For Mantle Cell Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20, and a BTK inhibitor.

• NOTE: Prior CD19 directed CART must have a 100-day washout period.

⁃ For Marginal Zone Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20.

• NOTE: Prior CD19 directed CART must have a 100-day washout period.

⁃ For Large B cell Lymphoma, patients must have received ≥ two prior lines of therapy, including an antibody directed against CD20. Prior exposure to CD19 directed CART will be allowed at the discretion of the Principal Investigator.

• NOTE: Prior failed CD19 directed CART must have a 100-day washout period

⁃ For Richter's Transformation, patients must have received ≥two prior lines of therapy, including an antibody directed against CD20.

⁃ 100-day washout period starts from the date of the last prior CAR-T infusion.

• PRE-REGISTRATION: Measurable disease

• REGISTRATION: Positive BAFFR test

• REGISTRATION: Measurable disease

• REGISTRATION: Eastern Cooperative Oncology Group (ECOG) performance status 0, 1 or 2

• REGISTRATION: Hemoglobin ≥ 9.0 g/dL (unless due to documented marrow involvement with disease) obtained ≤14 days prior to registration

• REGISTRATION: Absolute neutrophil count (ANC) ≥ 1500/mm\^3 (unless due to documented marrow involvement with disease) obtained ≤14 days prior to registration

• REGISTRATION: Platelet count ≥100,000/mm\^3 (unless due to documented marrow involvement with disease) obtained ≤ 14 days prior to registration

• REGISTRATION: Total bilirubin ≤ 1.5 x upper limits of normal (ULN) (Subjects with Gilbert's Syndrome may be included if their total bilirubin is ≤ 3.0 x ULN and direct bilirubin ≤ 1.5 x ULN) obtained ≤ 14 days prior to registration

• REGISTRATION: Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤ 3 x ULN (≤ 5 x ULN for patients with liver involvement) obtained ≤ 14 days prior to registration

• REGISTRATION: Prothrombin time (PT)/international normalized ratio (INR) /activated partial thromboplastin time (aPTT) ≤ 1.5 x ULN OR if patient is receiving anticoagulant therapy and INR or aPTT is within target range of therapy obtained ≤ 14 days prior to registration

‣ Patients on a stable, maintenance regimen of anticoagulant therapy for ≥ 30 days prior to registration may have PT/INR measurements \> 1.5 X ULN if, in the judgment of the investigator, the patient is suitable for the study

• REGISTRATION: Calculated creatinine clearance ≥45 ml/min using the Cockcroft-Gault formula obtained ≤ 14 days prior to registration

• REGISTRATION: Negative pregnancy test done ≤ 7 days prior to registration, for persons of childbearing potential only. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required

• REGISTRATION: Provide written informed consent understand and comply with protocol-required study procedures

• REGISTARTION: Patients must have an ejection fraction (EF) of ≥ 45%

• REGISTRATION: Patients must have pulse ox measurements of \> 92% on room air

• REGISTRATION: Willingness to provide mandatory blood specimens for correlative research

• REGISTRATION: Willing to return to enrolling institution for study follow-up