Axi-cel in CNS Lymphoma

Inclusion Criteria: * Patients with relapsed/refractory active primary or secondary CNS lymphoma, histologically proven aggressive B cell lymphoma, including DLBCL, HGBL, PMBL, or tFL, and defined by the following categories: * Primary CNS lymphoma, relapsed or refractory following at least one line of CNS-directed therapy. There is no restriction on the number of recurrences. * Secondary CNS lymphoma, relapsed or refractory following at least one line of CNS-directed therapy for prophylaxis or treatment of CNS lymphoma. * Radiographically event CNS disease by MRI of the brain (ie enhancing lesion on gadolinium enhanced MRI) * For patients with secondary CNSL with concurrent systemic lymphoma, the concurrent systemic lymphoma must be either DLBCL, PMBL, high grade B cell lymphoma, or transformed lymphoma and must have relapsed following at least 1 prior lines of therapy (which must have included an anti-CD20 monoclonal antibody (unless the tumor is CD20 negative) and an anthracycline * 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 * Age 18 years or older at the time of informed consent * ECOG performance status of 0 or 1 * Adequate bone marrow, renal, hepatic, pulmonary and cardiac function defined as: * Absolute neutrophil count (ANC) ≥1000/μL * Platelet count ≥ 75,000/μL * Absolute lymphocyte count ≥ 100/μL * Creatinine clearance (as estimated by Cockcroft Gault) ≥ 60 mL/min * Serum alanine aminotransferase/aspartate aminotransferase (ALT/AST) ≤ 2.5 upper limit of normal (ULN) * Total bilirubin ≤ 1.5 mg/dl, except in subjects with Gilbert's syndrome * Cardiac ejection fraction ≥ 50%, no clinically significant pericardial effusion as determined by an echocardiogram (ECHO), and no clinically significant electrocardiogram (ECG) findings * No clinically significant pleural effusion * Baseline oxygen saturation \> 92% on room air GCSF and transfusions are not allowed for eligibility determination.+++ * 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) Exclusion Criteria: * Primary vitreoretinal lymphoma and intraocular PCNSL without evidence of brain disease. Patients with prior history of intraocular involvement treated only with intraocular methotrexate and no prior systemic therapy are excluded * PCNSL patients who cannot undergo magnetic resonance imaging assessments * Patients with brain stem lesions * Patients with leptomeningeal disease only without brain parenchymal involvement * Bulky leptomeningeal disease and or CSF protein ≥100 mg/dL * History of malignancy other than nonmelanoma skin cancer or carcinoma in situ (eg cervix, bladder, breast) unless disease free for at least 3 years * History of Richter's transformation of CLL * History of allogeneic stem cell transplant * Prior CD19 targeted therapy * 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 first dose of axicabtagene ciloleucel or SOC * Prior chimeric antigen receptor therapy or other genetically modified T-cell therapy * History of severe, immediate hypersensitivity reaction attributed to aminoglycosides * 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. * 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. * Active tuberculosis * History or presence of non-malignant CNS disorder such as seizure disorder, cerebrovascular ischemia/hemorrhage, dementia, cerebellar disease, or any autoimmune disease with CNS involvement * Subjects with cardiac atrial or cardiac ventricular lymphoma involvement * 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 * Requirement for urgent therapy due to tumor mass effects * History of autoimmune disease, requiring systemic immunosuppression and/or systemic disease modifying agents within the last 12 months. * History of idiopathic pulmonary fibrosis, organizing pneumonia (eg, 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. * History of symptomatic deep vein thrombosis or pulmonary embolism requiring ongoing systemic anticoagulation * Any medical condition likely to interfere with assessment of safety or efficacy of study treatment * History of severe immediate hypersensitivity reaction to tocilizumab or any of the agents used in this study * 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 * Women of childbearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of chemotherapy on the fetus or infant. Subjects of either sex who are not willing to practice birth control from the time of consent and at least 6 months after the last dose of axicabtagene ciloleucel or SOC chemotherapy * In the investigators judgment, the subject is unlikely to complete all protocol-required study visits or procedures, including follow-up visits, or comply with the study requirements for participation.