Inclusion Criteria:
1. Age ≥ 18 years old.
2. Able to understand and provide a signed informed consent that fulfills the relevant Human Research Ethics Committee (HREC) or Independent Ethics Committee (IEC) guidelines.
3. Histologically documented CD19- and CD20-positive B-cell NHL (excluding primary CNS lymphoma, CLL, and Burkitt lymphoma) with the following specific criteria:
1. Have completed ≥ 2 lines of cytotoxic chemotherapy.
2. Have received rituximab or another anti-CD20 antibody.
3. Have measurable disease by Lugano classification documented within 8 weeks of the time of consent, defined as nodal lesions \> 15 mm in the long axis or extranodal lesions \> 10 mm in long and short axis, or bone marrow involvement that is biopsy proven.
4. Have CD19- and CD20-positive disease confirmed on the diagnostic or repeat biopsy specimen. A minimum of 5% CD19 and CD20 positivity by immunohistochemistry or flow cytometry is required.
4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1.
5. Expected survival \> 16 weeks.
6. Stated willingness to comply with study procedures.
7. Able to attend required study visits and return for adequate followup, as required by this protocol.
8. Agreement to practice effective contraception for female participants of childbearing potential and nonsterile males. Female participants of childbearing potential must agree to use effective contraception while on study and for at least 5 months after the last dose of study drug. Nonsterile male participants must agree to use a condom while on study and for up to 5 months after the last dose of study drug. Effective contraception includes surgical sterilization (eg, vasectomy, tubal ligation), two forms of barrier methods (eg, condom, diaphragm), and intrauterine devices (IUDs).
Exclusion Criteria:
1. Histologically documented primary CNS lymphoma, CLL, Burkitt, or Burkitt-like lymphoma.
2. Known hypersensitivity to sulfa-containing study medication(s), including anaphylactic reaction to sulfa-containing medications.
3. Known allergy to albumin (human) or dimethyl sulfoxide (DMSO).
4. Serious uncontrolled concomitant disease that would contraindicate the use of the investigational drug used in this study or that would put the participant at high risk for treatment related complications.
5. History of significant autoimmune disease OR active, uncontrolled autoimmune phenomenon: such as systemic lupus erythematous, Wegner's glomerulonephritis, autoimmune hemolytic anemia, idiopathic thrombocytopenic purpura requiring steroid therapy defined as \> 20 mg of prednisone or equivalent daily.
6. History of allogeneic hematopoietic stem-cell transplantation (HSCT) requiring ongoing systemic graft versus host disease (GvHD) therapy.
7. Anti-CD20 antibody treatment less than 2 weeks prior to cell infusion.
8. History of receiving allograft organ transplant requiring immunosuppression.
9. Participants post solid organ transplant who develop high grade lymphomas or leukemias.
10. CD19- and CD20-positive metastases to the CNS, including the parenchyma
11. Nonmalignant CNS disease (eg, stroke, epilepsy, vasculitis, or neurodegenerative disease).
12. History of or active inflammatory bowel disease (eg, Crohn's disease, ulcerative colitis).
13. Inadequate organ function, evidenced by the following laboratory results:
1. ANC \< 1000 cells/mm3.
2. Platelet count \< 100,000 cells/mm3.
3. Total bilirubin ≥ 1.5 × the upper limit of normal (ULN; unless the participant has documented Gilbert's syndrome or indirect hyperbilirubinemia).
4. Aspartate aminotransferase (AST \[SGOT\]/ALT (SGPT) ≥ 2.5 × ULN.
5. Alkaline phosphatase (ALP) levels ≥ 2.5 × ULN (or ≥ 5 × ULN in participants with bone metastases).
6. Serum creatinine \> 1.6 mg/dL.
7. Each study site should use its institutional ULN to determine eligibility.
14. Uncontrolled hypertension (systolic \> 160 mm Hg and/or diastolic \> 110 mm Hg) or clinically significant (ie, active) cardiovascular disease, cerebrovascular accident/stroke, or myocardial infarction within 6 months prior to first study medication; unstable angina; congestive heart failure of New York Heart Association grade 2 or higher; or serious cardiac arrhythmia requiring medication.
15. Current chronic daily treatment (continuous for \> 3 months) with systemic corticosteroids defined as \> 20 mg of prednisone or equivalent daily, excluding inhaled steroids. Short-term steroid use to prevent IV contrast allergic reaction or anaphylaxis in participants who have known contrast allergies is allowed.
16. Currently taking any medication(s) (herbal or prescribed) known to have an adverse drug reaction with any of the study medications.
17. Tested positive for tuberculosis (TB) utilizing the QuantiFERON Gold TB test.
18. History of human immunodeficiency virus (HIV) with current CD4+ T-cell count \< 350 cells/μL and a detectable HIV viral load.
19. Known carriers of hepatitis B virus (HBV) infection that is currently hepatitis B surface antigen (HBsAg) positive.
20. Concurrent active malignancy other than basal or squamous cell carcinomas of the skin.
21. Assessed by the Investigator to be unable or unwilling to comply with the requirements of the protocol.
22. Women who are pregnant or breastfeeding
