Optimizing lymphoDepletion to Improve Outcomes In Patients Receiving Cell Therapy With Yescarta

Inclusion Criteria: 1. Age ≥ 18 years at the time of informed consent 2. Life expectancy ≥ 12 weeks 3. Biopsy-proven and histologically confirmed R/R large B cell lymphoma, including R/R DLBCL, transformation from FL, and R/R PMBCL. 4. Radiographically documented measurable disease as per Lugano response criteria (i.e. LDi \> 1.5 cm that is FDG avid). 5. At least 2 weeks or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic cancer therapy at the time the subject provides consent 6. Eligible for standard of care CAR T cell therapy, specifically, relapsed or refractory large B cell lymphoma after two or more lines of systemic therapy, and subjects must have received adequate first-line therapy including at a minimum: * Anti-CD20 monoclonal antibody unless investigator determines that tumor is CD20 negative, and * An anthracycline containing chemotherapy regimen 7. Patient does not have active CNS disease 8. Patient is sufficiently stable to facilitate planned CAR T-cell therapy (e.g. not rapidly progressing on temporizing therapy, no significant compromise of vital organ functions (intubation, dialysis, requiring ICU/vasopressor support)) and has good performance status 9. ECOG performance status 0 or 1 at enrollment 10. Patient has not received prior adoptive T-cell immunotherapy 11. Patient is not HIV positive 12. Patient did not receive prior allogeneic stem cell transplant 13. Adequate bone marrow, renal, hepatic, pulmonary and cardiac function 14. Females of childbearing potential must have a negative serum or urine pregnancy test (females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential) 15. Sexually active males who accept to use a condom during intercourse during treatment and for 6 months after treatment as they should not father a child in this period. A condom is required to be used also by vasectomized men (as well as during intercourse with a male partner) in order to prevent delivery of the drug via seminal fluid 16. Must have an apheresis product of non-mobilized cells accepted for manufacturing. Exclusion Criteria: 1. Persisting disease bulk (defined as ≥10 cm) on restaging imaging following bridging therapy. 2. History of malignancy other than nonmelanoma skin cancer or carcinoma in situ (e.g. cervix, bladder, breast) unless disease free for at least 3 years 3. History of Richter's transformation of CLL 4. History of allogeneic stem cell transplant 5. Received \< 2 lines of therapy for large B cell lymphoma 6. Prior CD19 targeted therapy 7. Subject has received or undergone the following: o Therapeutic doses of corticosteroids (defined as \>20 mg/day prednisone or equivalent) within 7 days prior to leukapheresis. Physiologic steroid replacement, topical, and inhaled steroids are permitted. * Cytotoxic chemotherapeutic agents that are not considered lymphotoxic, and intrathecal (IT) chemotherapy must be stopped ≥ 7 days prior to leukapheresis. * Lymphotoxic chemotherapeutic agents (eg, cyclophosphamide \> 300 mg/m2, ifosfamide, bendamustine) 4 weeks prior to leukapheresis. * Experimental agents within 4 weeks prior to signing the ICF, unless no response or PD is documented on the experimental therapy and at least 5 half-lives have elapsed prior to leukapheresis. * Ibrutinib, lenalidomide and PI3K inhibitor within 5 half-lives prior to leukapheresis * Immunosuppressive therapies within 4 weeks prior to leukapheresis (eg, calcineurin inhibitors, methotrexate or other chemotherapeutics, mycophenolate, rapamycin thalidomide, immunosuppressive antibodies such as anti-tumor necrosis factor \[TNF\], anti-IL6, or anti- IL6R) * Radiation within 6 weeks of leukapheresis. Subject must have progressive disease in irradiated lesions or have additional nonirradiated, PET-positive lesions to be eligible. Radiation to a single lesion, if additional non-irradiated PET-positive lesions are present, is allowed up to 2 weeks prior to leukapheresis (discuss with sponsor). * Treatment with systemic immunostimulatory agents (including but not limited to interferon and IL-2) within 6 weeks or 5 half-lives of the drug, whichever is shorter, prior to the infusion of axicabtagene ciloleucel 8. Prior chimeric antigen receptor therapy or other genetically modified T-cell therapy 9. Presence of fungal, bacterial, viral, or other infection that is uncontrolled or requiring intravenous (IV) antimicrobials for management. Simple urinary tract infection (UTI) and uncomplicated bacterial pharyngitis are permitted if responding to active treatment. 10. Known history of infection with human immunodeficiency virus (HIV) or hepatitis B (HBsAg positive) or hepatitis C virus (anti-HCV positive). If there is a positive history of treated hepatitis B or hepatitis C, the viral load must be undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing. 11. Active tuberculosis 12. Presence of any indwelling line or drain (eg, percutaneous nephrostomy tube, indwelling Foley catheter, biliary drain, or pleural/peritoneal/pericardial catheter). Dedicated central venous access catheters such as a Port-a-Cath or Hickman catheter are permitted 13. Subjects with detectable cerebrospinal fluid malignant cells or known CNS involvement; a history of prior treated CNS lymphoma which is not active at the time of relapse is permitted 14. History or presence of significant non-malignant CNS disorder such as seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or any autoimmune disease with CNS involvement 15. Subjects with cardiac atrial or cardiac ventricular lymphoma involvement 16. History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, New York Heart Association Class II or greater congestive heart failure, or other clinically significant cardiac disease within 12 months of enrollment 17. Requirement for urgent therapy due to tumor mass effects such as bowel obstruction or blood vessel compression 18. History of autoimmune disease, requiring systemic immunosuppression and/or systemic disease modifying agents within the last 2 years. 19. History of idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis per chest computed tomography (CT) scan at screening. History of radiation pneumonitis in the radiation field (fibrosis) is allowed. 20. History of symptomatic deep vein thrombosis or pulmonary embolism within 6 months of enrollment 21. Any medical condition likely to interfere with assessment of safety or efficacy of study treatment 22. History of severe immediate hypersensitivity reaction to tocilizumab or any of the agents used in this study 23. Treatment with a live, attenuated vaccine within 6 weeks prior to initiation of study treatment, or anticipation of need for such a vaccine during the course of the study 24. Women of childbearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of chemotherapy on the fetus or infant. 25. Subjects of either sex who are not willing to practice birth control from the time of consent and at least 6 months after axicabtagene ciloleucel infusion 26. In the investigators judgment, the subject is unlikely to complete all protocol- required study visits or procedures, including followup visits, or comply with the study requirements for participation.