Study to Assess Safety, Tolerability and Efficacy of MB-106 in Patients With Relapsed or Refractory B-Cell NHL or CLL

Inclusion Criteria: 1. For Phase 1: Patient must have relapsed or refractory B-cell NHL (with the exception of Burkitt lymphoma and lymphoblastic lymphoma) or CLL that has progressed after standard therapies, including chemotherapy and anti-CD20 antibody combinations and molecularly targeted therapies. Patients may also have undergone prior stem cell transplant and/or prior CD19-directed CAR-T cell therapy. 2. For Phase 2: Patient must have the following: * Arm 1E: Relapsed or refractory DLBCL, including high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements, primary mediastinal large B-cell lymphoma and transformed FL. All patients must have progressed after at least 2 lines of therapy, including induction therapy with an anthracycline-based regimen with anti-CD20 antibody, as well as a second systemic therapy. Patients may have also received prior stem cell transplant and/or CD19-directed CAR-T therapy. * Arm 2E: Relapsed or refractory FL. All patients must have progressed after at least 2 lines of therapy. Patients may have also received prior stem cell transplant and/or CD19-directed CAR-T therapy. * Arm 2E-Basket: Relapsed or refractory B-cell NHL subtypes that have progressed after available therapies. This "basket" arm will include but is not limited to MCL, MZL, WMG, Burkitt and Burkitt-like lymphoma, and HCL. Patients may have also received prior stem cell transplant and/or CD19-directed CAR-T therapy. * Arm 3E: Relapsed or refractory CLL/SLL All patients must have progressed after prior Bruton's tyrosine kinase (BTK) and/or BCL-2 directed therapy. Patients may have also progressed or have been intolerant to prior BTK and anti-CD20 antibody therapy. Patients may have also received prior stem cell transplant and/or CD19 CAR-T therapy. 3. For patients treated with prior CD19-directed CAR-T therapy (all arms): relapsed from PR or CR of ≥ 3 months' duration with CD19-positive or -negative disease, or relapsed from PR or CR at any time with CD19-negative disease. 4. For patients treated with prior CD19-directed CAR-T therapy, the peripheral blood absolute CD19+ B-cell count, as measured by flow cytometry, has recovered to at least 20 cells/μl. 5. For patients with NHL, at least 1 measurable lesion according to the revised International Working Group Response Criteria for Malignant Lymphoma. Patients with Waldenstrom macroglobulinemia may qualify for enrollment based on a measurable lesion or an elevated IgM level \>0.5 g/dL. 6. For patients with CLL, diagnosis of CLL that meets published diagnostic criteria. Measurable disease is not required. 7. Evidence of CD20 expression on the tumor specimen obtained from the original diagnostic biopsy or another tissue biopsy performed prior to enrollment into this study. 8. At least 2 weeks or 5 half-lives, whichever is shorter, have elapsed since any prior non-investigational systemic therapy before the patient's planned leukapheresis, with the exception of prior BTK inhibitor therapy, which can continue until day -6 (1 day prior to lymphodepletion). At least 6 months have elapsed since the last administration of bendamustine before patient's planned leukapheresis. 9. Males and females ≥18 years of age at the time of consent. 10. Capable of understanding, willing to comply with, and voluntarily sign and date an informed consent form prior to the conduct of any study related assessments/procedures. 11. Able to adhere to the study visit schedule and other protocol requirements. 12. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 13. Life expectancy of ≥ 16 weeks, as assessed by the Principal Investigator. 14. All patients must meet all of the following laboratory criteria unless, in the opinion of the Investigator, the cytopenias are considered to be the result of bone marrow infiltration by lymphoma/CLL: * Absolute neutrophil count (ANC) ≥ 0.75×10e9/L. * Platelet count ≥ 75×10e9/L. * Hemoglobin ≥ 8.5 g/dL. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5× the upper limit of normal (ULN). * Calculated creatinine clearance ≥ 45.0 mL/minute as estimated by Cockcroft-Gault formula. * Total bilirubin ≤ 1.5×upper limit of normal (ULN), unless due to suspected Gilbert's syndrome. 15. Adequate pulmonary function, defined as ≤ Grade 1 dyspnea and oxygen saturation (SaO2) ≥ 92% on room air. If pulmonary function tests (PFTs) are performed based on the clinical judgment of the treating physician, patients with forced expiratory volume in 1 second (FEV1) ≥ 50% of predicted and diffusing capacity for carbon monoxide (DLCO) (corrected) of ≥ 40% of predicted will be eligible. 16. Left ventricular ejection fraction ≥ 50%, as determined by echocardiography (ECHO) or multi-gated acquisition scan (MUGA). 17. Females of childbearing potential must have a negative serum or urine pregnancy test at screening and a negative serum or urine pregnancy test prior to initiation of the lymphodepletion regimen. 18. If procreative potential exists, patient must agree to use a highly effective method of contraception from the start of the study until 1 year after the completion of lymphodepletion for females and 4 months after completion of lymphodepletion for males. Exclusion Criteria: * Patients who meet ANY of the following criteria will be excluded from the study. No exemptions will be granted.: 1. Previous treatment with anti-CD20 or anti-CD19 therapy (including antibodies, antibody-drug conjugates \[ADCs\], bispecific antibodies, etc.) or any investigational agent within 4 weeks before leukapheresis. 2. Concurrent known additional malignancy that is progressing and/or requires active treatment. Exceptions include squamous or basal cell carcinoma of the skin, superficial bladder cancer, and prostate cancer not requiring treatment. 3. Presence of active acute or chronic Graft versus Host Disease (GVHD). 4. Active central nervous system (CNS) lymphoma, including primary CNS lymphoma. 5. Corticosteroid dependence on doses greater than physiological replacement, i.e., requirement for prednisone \> 7.5 mg/day or hydrocortisone ≥ 12 mg/m2/day. 6. Ongoing prior therapy-related toxicities ≥ Grade 2, according to the Common Toxicity Criteria for Adverse Events (CTCAE), version 5.0, with the exception of alopecia or vitiligo or Grade 2 peripheral neuropathy. 7. Active systemic infections, active, uncontrolled coagulation or bleeding disorders, or other active, uncontrolled major medical illnesses of the respiratory or immune system. * Simple upper respiratory tract infection, uncomplicated bacterial pharyngitis and/or urinary tract infection are permitted if responding to active treatment and after consultation with the study Medical Monitor. 8. Cardiac involvement with lymphoma, including pericardial involvement and malignant pericardial effusion. 9. Significant cardiovascular diseases within the past 6 months including uncontrolled congestive heart failure (\>New York Heart Association class II), myocardial infarction, unstable angina, or uncontrolled arrhythmia. However, patients with ischemic heart disease who have had acute coronary syndrome, myocardial infarction and/or revascularization \> 6 months before Screening, who are without cardiac symptoms, may enroll. 10. Requirement for urgent therapy due to tumor mass effects such as bowel obstruction or blood vessel compression. 11. Documented human immunodeficiency virus (HIV) infection or any form of primary immunodeficiency, such as severe combined immunodeficiency disease. 12. Known active infection with hepatitis B, hepatitis C, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), or other viral infections requiring systemic therapy. 13. History of autoimmune disease (e.g., Crohn's disease, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the previous 2 years. 14. If female, pregnant, planning to become pregnant, or breastfeeding. 15. Any other clinically significant medical disease or condition that, in the Principal Investigator's opinion, may interfere with protocol adherence or the patient's ability to provide informed consent.