Study for Subjects With Relapsed/Refractory Non- Hodgkin Lymphoma

Inclusion Criteria: 1. Age ≥ 18 years old. 2. Able to understand and provide a signed informed consent that fulfills the relevant Institutional Review Board (IRB) or Independent Ethics Committee (IEC) guidelines. 3. Histologically documented CD19- and CD20-positive B-cell NHL with the following specific criteria: 1. Have active disease after ≥ 2 lines of cytotoxic chemotherapy. 2. Have received rituximab or another anti-CD20 antibody. 3. Have either failed autologous transplant or are ineligible to receive autologous transplant. 4. 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. 5. Have CD19- and CD20-positive disease on most recent biopsy performed (a repeat biopsy is not mandatory for this study except as noted below). A minimum of 5% CD19 and CD20 positivity by immunohistochemistry or flow cytometry on prior or repeat biopsy is required. 4. History of central nervous system (CNS) involvement with cerebral spinal fluid (CSF) analysis following magnetic resonance imaging (MRI) brain and lumbar puncture showing no evidence of CNS involvement by cytology and flow cytometry. 5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. 6. Expected survival \> 12 weeks. 7. Willing and able to have central line placed for study drug infusions. 8. Stated willingness to comply with study procedures. 9. Able to attend required study visits and return for adequate follow-up, as required by this protocol. 10. Agreement to practice effective contraception for female subjects of child-bearing potential and nonsterile males. Female subjects of child-bearing 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 subjects 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) used with spermicide, intrauterine devices (IUDs), and abstinence. Exclusion Criteria: 1. Known hypersensitivity to any component of the study medication(s), including anaphylactic reaction to sulfur-containing medications. 2. Known allergy to albumin (human) or dimethyl sulfoxide (DMSO). 3. Serious uncontrolled concomitant disease that would contraindicate the use of the investigational drug used in this study or that would put the subject at high risk for treatment-related complications. 4. 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. 5. History of allogeneic hematopoietic stem-cell transplantation (HSCT) or allogeneic chimeric antigen receptor (CAR) T therapy within 6 months of day 1 or require ongoing systemic graft versus host disease (GvHD) therapy. 6. Anti-CD19 or anti-CD20 antibody treatment within 4 weeks of cell infusion. 7. Live vaccine \< 6 weeks prior to starting lymphodepleting chemotherapy. 8. History of receiving allograft organ transplant requiring immunosuppression. 9. Subjects post solid organ transplant who develop high grade lymphomas or leukemias. 10. Known lymphomatous involvement of the CNS, including the parenchyma or leptomeninges. 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 subject 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 subjects with bone metastases). 6. Serum creatinine \> 1.6 mg/dL. 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 (dose equivalent to or greater than 10 mg/day methylprednisolone), excluding inhaled steroids. Short-term steroid use to prevent IV contrast allergic reaction or anaphylaxis in subjects 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. History of human immunodeficiency virus (HIV) with current CD4+ T-cell count \< 500 cells/μL.. 18. Chronic carriers of hepatitis B virus (HBV) infection that is currently hepatitis B surface antigen (HBsAg) positive. NOTE: Subjects who have a history of HIV/HBV or who are seropositive will require testing for Infectious Disease Markers (IDM). 19. Concurrent active malignancy other than basal or squamous cell carcinomas of the skin. 20. Assessed by the Investigator to be unable or unwilling to comply with the requirements of the protocol. 21. Women who are pregnant or breastfeeding. A negative urine or serum pregnancy test in women of child bearing potential is required at screening and again within 48 hours prior to lymphodepleting chemotherapy