GENERAL INCLUSION CRITERIA FOR ALL PATIENTS

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

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

          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.

          4. 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.

          5. Karnofsky performance score ≥70.

          6. 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.

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

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

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

               1. No IV hydration within 24 hours of eligibility.

               2. No dialysis dependent renal failure within three months of planned CAR infusion.

         10. Able to provide written informed consent.

         11. Agree to practice birth control during the study.

         12. 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%.

         13. Expected survival >12 weeks.

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

         15. Meet criteria regarding fertility and contraception.

         16. No contraindication to central line access.

         17. Patient has demonstrated compliance to other therapies.

        Phase 1: 3+3 COHORT ELEGIBILITY CRITERIA

          1. 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).

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

               1. 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.

               2. Relapse post-autologous transplant

               3. Relapse post-allogeneic transplant

               4. Patients not previously treated with CAR-T cell therapy

        PHASE 1b and 2 COHORT ELEGIBILITY CRITERIA

        COHORT 1: Six to nine patient expansion with 8-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,
        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:

          1. 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.

          2. Relapse post-autologous transplant.

          3. Relapse post-allogeneic transplant.

          4. 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.

        COHORT 2: 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:

               1. 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.

               2. Relapse post-autologous transplant.

               3. Relapse post-allogeneic transplant.

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

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

        COHORT 3: Mantle Cell Lymphoma (Phase 2) 1. Diagnosis of Mantle Cell Lymphoma. 2. Patients
        must have active, measurable disease as previously designed and have relapsed, refractory
        disease as defined as one of the following:

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

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

          3. Relapse post-autologous transplant.

          4. Relapse post-allogeneic transplant.

          5. 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.

        Exclusion Criteria (all patients) A potential subject who meets any of the following
        exclusion criteria is ineligible to participate in the study.

          1. Positive beta- human chorionic gonadotropin (HCG) in female of childbearing potential.

          2. Confirmed active human immunodeficiency virus (HIV), Hepatitis B or C infection.

          3. History of significant autoimmune disease OR active, uncontrolled autoimmune
             phenomenon requiring steroid therapy defined as >20 mg of prednisone or equivalent
             daily.

          4. Presence of ≥grade 3 non-hematologic toxicities as per CTCAE version 5.0 from any
             previous treatment unless it is felt to be due to underlying disease.

          5. Concurrent use of investigational therapeutic agents or enrollment on another
             therapeutic clinical trial at any institution. Minimum of 14 days or 5 half-lives of
             the drug (whichever is shorter) washout prior to apheresis.

          6. Refusal to participate in the long-term follow-up protocol

          7. Patients with active CNS involvement by malignancy on MRI or by lumbar puncture.

             a. Patients with prior CNS disease that has been effectively treated will be eligible
             providing treatment was >4 weeks before enrollment and a remission documented within 8
             weeks of planned CAR-T cell infusion by MRI brain and CSF analysis.

          8. Previous recipients of allogeneic hematopoietic stem cell transplantation (AHCT) are
             excluded if they are <100 days' post-transplant, have evidence of active
             graft-versus-host-disease (GVHD) of any grade, or are currently on immunosuppression.

          9. Prior allogeneic CAR T-cell therapy

         10. Previous recipients of autologous CAR-T cell therapy directed at either CD19 or CD20
             are excluded if they are <100 days post prior CAR-T cell treatment (does not include
             re-enrollment) or have >5% residual circulating CAR-T as measured by flow cytometry
             using a CD19 CAR detection reagent (Miltenyi Biotec)

             a. Patients with prior CAR-T treatment against CD19 or CD20 must have repeat biopsy
             post-CAR-T cell therapy confirming a minimum of 5% CD19 or CD20 positivity by
             immunohistochemistry or flow cytometry

         11. Anti-CD20 antibody treatment within 4 weeks of cell infusion

         12. Anti-CD19 antibody treatment within 4 weeks of cell infusion

         13. Cytotoxic chemotherapy other than lymphodepletion within 14 days of CAR-T cell
             infusion

         14. Cytotoxic chemotherapy treatment within 14 days or steroid treatment (other than
             replacement dose steroids) within 7 days prior to apheresis collection for CAR-T cells

         15. Oral chemotherapeutic agents or antibody directed treatment within 7 days of apheresis

             a. BTK inhibitors are allowed until 1-day prior to apheresis and can re-start until
             1-day prior to lymphodepletion

         16. Patients post solid organ transplant who develop high grade lymphomas or leukemias

         17. Concurrent active malignancy other than basal or squamous cell carcinomas of the skin
             (underlying low-grade lymphoma chronic lymphocytic leukemia/follicular lymphoma
             (FL)/marginal zone lymphoma (MZL) is allowable in patients with transformed large cell
             lymphoma)