Inclusion Criteria:

          1. Patients with CLL or SLL with radiographically measurable disease

               -  Cohort 2 only: patients with progressed or progressing CLL/SLL on ibrutinib or
                  acalabrutinib with del 17p and/or TP53 mutated

               -  Cohort 3 only: patients with progressed or progressing CLL/SLL on ibrutinib or
                  acalabrutinib without del 17p and/or TP53 mutated

          2. Patients must have documented progression or be progressing on ibrutinib or
             acalabrutinib, as indicated by the presence of known BTK resistance mutation

          3. Patients must have received at least 1 prior regimen (only for patients without del
             17p and/or TP53 mutated) and currently be on ibrutinib or acalabrutinib. For patients
             on combination therapy as the last line of therapy prior study entry, progression to
             any of the individual components of the combination therapy, rather than to the
             combination regimen, is required.

               -  For Cohort 2: The single prior regimen can be ibrutinib or acalabrutinib (ie,
                  patients are eligible while progressing on their first line of therapy)

               -  For Cohort 3: Patients must have progressed on at least 1 additional line of
                  therapy in addition to ibrutinib or acalabrutinib

          4. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of
             0 or 1 and an estimated life expectancy of ≥ 3 months.

          5. Patients must have adequate bone marrow function to receive NMA-LD

          6. Pulmonary function assessed by spirometry demonstrating FEV1 > 50% predicted normal

          7. Cardiac function demonstrating left ventricular ejection fraction (LVEF) > 45%

          8. Patients of childbearing potential or their partners of childbearing potential must be
             willing to practice an approved method of birth control during treatment and for 12
             months after receiving the last protocol-related therapy.

        Exclusion Criteria:

          1. Patients who have received an organ allograft or prior cell transfer therapy within 20
             years.

          2. Patients with known or suspected transformed disease (ie, Richter's Transformation).

          3. Patients who received treatment with any systemic chemotherapy, immunotherapy,
             targeted small molecule inhibitors, or other biologic agents within 30 days or 5
             half-lives, whichever is shorter, of IOV-2001 infusion with the exception of ibrutinib
             or acalabrutinib

          4. Patients with known involvement of central nervous system (CNS) by lymphoma or
             leukemia

          5. Patients who are on chronic systemic steroid therapy >5 mg/day prednisone equivalent
             for any reason

          6. Patients who have active systemic infections requiring systemic ABX, autoimmune anemia
             or thrombocytopenia, coagulation disorders, or other active major medical illnesses of
             the cardiovascular, respiratory, or immune system.

          7. Patients who are seropositive for any of the following:

               -  Human immunodeficiency virus (HIV)-1 or HIV-2 antibodies

               -  Hepatitis B antigen (HbsAg) or anti-hepatitis B core total antibodies
                  (anti-HbcAb), or hepatitis C antibody (HCVAb)

          8. Patients with active and chronic fungal, bacterial, or viral infection requiring IV
             treatment

          9. Patients who require treatment for anti-coagulation with a vitamin K antagonist
             (warfarin)

         10. Patients who have received a live or attenuated vaccine within 28 days of beginning
             the preparative NMA-LD regimen

         11. Patients who are pregnant or breastfeeding