• Patients must be aged ≥18 years and ≤80 years with relapsed or refractory B-cell non-Hodgkin Lymphoma.

• Absolute cluster of differentiation 3 (CD3) count ≥50 mm\^3.

• Magnetic resonance imaging (MRI) brain and lumbar puncture with cerebrospinal fluid (CSF) analysis by cytology and flow cytometry without evidence of central nervous system (CNS) involvement ONLY in patients with history of CNS involvement or clinical suspicion at the time of enrollment EXCEPT Arm E subjects.

• Measurable disease must be documented within four weeks of the time of consent defined as nodal lesions greater than 15 mm in the long axis or extranodal lesions \>10 mm in long and short axis OR bone marrow involvement that is biopsy proven for B-cell NHL (see separate criteria for CLL and primary/secondary CNS lymphoma).

• Karnofsky performance score ≥70.

• Adequate hepatic function, defined as aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \<5 x upper limit of normal (ULN); serum bilirubin and alkaline phosphatase \<5 x ULN, or considered not clinically significant as per the clinical PIs discretion (e.g. Gilbert's or indirect hyperbilirubinemia) or felt to be due to underlying disease.

• ANC≥1000 with no G-CSF within 72 hours or pegylated G-CSF within 14 days.

• Platelets≥50,000 with no transfusion within 72 hours.

• Adequate renal function, defined as creatinine clearance \>60 ml/min AND serum Cr≤1.5 mg/dL.

• a. No IV hydration within 24 hours of eligibility. b. No dialysis dependent renal failure within three months of planned CAR infusion.

⁃ Able to provide written informed consent.

⁃ Agree to practice birth control during the study.

⁃ Adequate cardiac function as indicated by New York Heart Association (NYHA) classification I or II AND left ventricular ejection fraction of ≥45% (by cardiac echocardiogram (ECHO) or multigated acquisition scan (MUGA)) and adequate pulmonary function as indicated by room air oxygen saturation of ≥92%.

⁃ Expected survival \>12 weeks.

⁃ Negative urine or serum pregnancy test in females of child bearing potential at study entry.

⁃ Meet criteria regarding fertility and contraception.

⁃ No contraindication to central line access.

⁃ Patient has demonstrated compliance to other therapies.

• Phase 1: 3+3 COHORT ELEGIBILITY CRITERIA

• Diagnosis of B-cell NHL including Follicular Lymphoma, Marginal Zone Lymphoma (splenic, nodal, extranodal), Mantle Cell Lymphoma, and DLBCL with associated subtypes (aggressive B-cell lymphoma, high grade B-cell lymphoma, T-cell/histocyte rich B-cell lymphoma, primary mediastinal B-cell lymphoma, Epstein-Barr virus-positive (EBV+) diffuse large B-cell lymphoma, transformed lymphoma such as transformed follicular or marginal zone, and Richter's transformation).

• Patients must have active, measurable disease as defined and meet one of the following criteria.

∙ Must have received Rituximab or another cluster of differentiation 20 (CD20) antibody and at minimum two different chemotherapy regimens appropriate for their disease and be ineligible to receive autologous transplant.

‣ Relapse post-autologous transplant

‣ Relapse post-allogeneic transplant

‣ Patients not previously treated with CAR-T cell therapy

• PHASE 1b and 2 COHORT ELEGIBILITY CRITERIA

• ARM A: Six to nine patient expansion with 8-day manufacturing (Phase 1b)

• Diagnosis of B-cell NHL including Follicular Lymphoma, Marginal Zone Lymphoma (splenic, nodal, extranodal), and DLBCL with associated subtypes (aggressive B-cell lymphoma, T-cell/histocyte rich B-cell lymphoma, primary mediastinal B-cell lymphoma, EBV+ diffuse large B-cell lymphoma, transformed lymphoma such as transformed follicular or marginal zone, and Richter's transformation).

• Patients must have active, measurable disease as defined and meet one of the following criteria:

∙ Must have received Rituximab or another cluster of differentiation 20 (CD20) antibody and at minimum two different chemotherapy regimens appropriate for their disease and be ineligible to receive autologous transplant.

‣ Relapse post-autologous transplant.

‣ Relapse post-allogeneic transplant.

‣ Relapse post-anti-cluster of differentiation 19 (CD19) CAR-T cell therapy.

• i. A maximum of two patients with prior CAR-T will be allowed in this cohort.

• ARM B: Six to nine patient expansion with 12-day manufacturing (Phase 1b)

• 1\. Diagnosis of B-cell NHL including Follicular Lymphoma, Marginal Zone Lymphoma (splenic, nodal, extranodal), and DLBCL with associated subtypes (aggressive B-cell lymphoma, high grade B-cell lymphoma, T-cell/histocyte rich B-cell lymphoma, primary mediastinal B-cell lymphoma, EBV+ diffuse large B-cell lymphoma, transformed lymphoma such as transformed follicular or marginal zone, and Richter's transformation).

• 2\. Patients must have active, measurable disease as defined and meet one of the following criteria:

• Must have received Rituximab or another CD20 antibody and at minimum two different chemotherapy regimens appropriate for their disease and be ineligible to receive autologous transplant.

• Relapse post-autologous transplant.

• Relapse post-allogeneic transplant.

• Relapse post-anti-CD19 CAR-T cell therapy.

• i. A maximum of two patients with prior CAR-T will be allowed in this cohort.

• ARM C: 24 patient cryopreservation 8/12 flexible manufacturing arm

• Diagnosis of B-cell NHL including Follicular Lymphoma, Marginal Zone Lymphoma (splenic, nodal, extranodal), and DLBCL with associated subtypes (aggressive B-cell lymphoma, high grade B-cell lymphoma, T-cell/histocyte rich B-cell lymphoma, primary mediastinal B-cell lymphoma, EBV+ diffuse large B-cell lymphoma, transformed lymphoma such as transformed follicular or marginal zone, and Richter's transformation).

• Patients must have active, measurable disease as defined and meet one of the following criteria a. Must have received Rituximab or another CD20 antibody and at minimum two different chemotherapy regimens appropriate for their disease and be ineligible to receive autologous transplant b. Relapse post-autologous transplant c. Relapse post-allogeneic transplant d. Relapse post-anti-CD19 CAR-T cell therapy i. A maximum of 2 patients with prior CAR-T will be allowed in this cohort

• ARM D: Phase 1 and Phase 1b: CLL

• 1\. Diagnosis of B-cell CLL or small lymphocytic leukemia (SLL) 2. Failed/progressed or been intolerant to two prior lines of therapy one of which MUST be either a covalent BTK inhibitor (e.g. ibrutinib, acalabrutinib, zanabrutinib, etc) or BCL2 inhibitors (e.g. venetoclax or other investigational BCL2) 3. Indication for treatment as defined as any of the following:

• measurable lymph nodes ≥ 1.5 cm in the greatest transverse diameter and/or hepatomegaly or splenomegaly)

• bone marrow involvement with ≥10% CLL involvement

• ARM E: Phase 1 and Phase1b Relapsed/Refractory Primary or Secondary CNS Lymphoma

• Diagnosis of diffuse large B cell lymphoma (DLBCL) with associated subtypes (aggressive B-cell lymphoma, high grade B-cell lymphoma, T-cell/histocyte rich B-cell lymphoma, primary mediastinal B-cell lymphoma, EBV+ diffuse large B-cell lymphoma, transformed lymphoma such as transformed follicular or marginal zone, and Richter's transformation) with secondary CNS lymphoma involvement OR primary CNS lymphoma.

• For Primary CNS lymphoma, relapsed or refractory following at least one line of CNS-directed therapy.

• Secondary CNS lymphoma relapsed or refractory following at least one line of CNS-directed therapy for treatment of CNS lymphoma.

∙ For patients with secondary central nervous system lymphoma (CNSL) with concurrent systemic lymphoma, the concurrent systemic lymphoma must have relapsed following at least 1 prior line of therapy (which must have included an anti-CD20 monoclonal antibody and an anthracycline)

• Measurable CNS disease by either lumbar puncture (LP) with positivity in CNS by flow cytometry or morphology for lymphoma cells OR magnetic resonance imaging (MRI) with enhancing lesions ≥1 cm in size consistent with lymphoma

• Must have had prior treatment with high dose methotrexate defined as methotrexate given intravenously at a dose ≥2500 mg/m\^2 and either progression/relapse, stable disease, or intolerance to at least one cycle of treatment.

• Phase II Cohort: Mantle Cell Lymphoma

• 1\. Diagnosis of Mantle Cell Lymphoma. 2. Patients must have active, measurable disease as previously defined and have relapsed, refractory disease as defined as one of the following:

• Relapsed disease after two lines of cytotoxic chemotherapy including administration of anti-CD20 antibody.

• Progressive disease after ≥second line Bruton tyrosine kinase (BTK) inhibitor.

• Relapse post-autologous transplant.

• Relapse post-allogeneic transplant.

• Relapse post anti-CD19 CAR-T cell therapy.

• i. A maximum of four patients with history of prior anti-CD19 CAR-T will be allowed in this cohort.