Experimental immune cell cocktail targets tough lymphoma

Copied word for word from the study's registry entry, so the wording is the study team's rather than ours.

Inclusion Criteria: * Age 18 years or older * Diagnosis of B-cell NHL (indolent and aggressive subtypes) including diffuse large B-cell lymphoma not otherwise specified (DLBCL NOS), high grade B-cell lymphoma (HGBCL), primary mediastinal B-cell lymphoma (PMBCL), follicular lymphoma (FL), chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL), marginal zone lymphoma (MZL), and mantle cell lymphoma (MCL) * Participants must have measurable disease as defined by Lugano 2014 criteria for NHL or iwCLL 2018 criteria for CLL. For NHL, measurable disease is defined as ≥1 measurable lesion (nodal or extra nodal) ≥1.5 cm in longest diameter by CT or PET/CT. For CLL, iwCLL criteria includes: presence of lymphocytosis (e.g., ALC ≥5 × 10⁹/L), lymphadenopathy ≥1.5 cm, and/or disease-related cytopenias (anemia, thrombocytopenia). * Relapsed and/or refractory after two or more lines of systemic therapy, including prior CD19 and/or CD20 directed therapies * For participants who have received a prior CD19 or CD20 directed therapy, the presence of CD19 and/or CD20 expression (by flow cytometry and/or immunohistochemistry) must be demonstrated on a post-treatment relapse biopsy * ECOG Performance Status \</= 2 * Preserved organ function as defined by: Total bilirubin \</= 1.5X upper limit of normal; AST/ALT \</= 2.5 X upper limit of normal; Calculated creatinine clearance \>/= 30mL/min estimated by Cockcroft Gualt formula; cardiac ejection fraction \>/= 45% and no more than mild/trace pericardial effusion on a recent echocardiogram; and adequate pulmonary function with oxygen saturation \>/= 92% on room air. * Participants must have the ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Second active malignancy (other than non-melanoma skin cancer or carcinoma in situ e.g. cervix, bladder, breast) that would confound interpretation of toxicity assessment or limit survival to prevent evaluation of therapy per discretion of principal investigator. Malignancies treated curatively or with hormonal therapy could be included after discussion with the principal investigator * Less than 28 days elapsed between prior treatment with investigational agent(s) and study enrollment * New York Heart Association class III-IV congestive heart failure * 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 * Known human immunodeficiency virus infection or acquired immunodeficiency syndrome related illness, except well controlled HIV with viral load \<200 copies/mL on antiretroviral therapy * Pregnant or breastfeeding women are excluded from this study because 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 NK cells, breastfeeding should be discontinued. These potential risks may also apply to other agents used in this study * Morphologic and/or cytogenetic features consistent with diagnosis of myelodysplastic syndrome on the most recent bone marrow biopsy prior to initiation of therapy * 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) * Participants with history of clinically relevant CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease * Active central nervous system or leptomeningeal involvement by lymphoma. 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 neurological 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 * History of active autoimmune disease (i.e. rheumatoid arthritis, systemic lupus erythematosus) with requirement of systemic immunosuppressive medications other than low dose steroids \[i.e. maximum of 15mg prednisone equivalent\] within the last 6 months