A Study of MB-CART19.1 Cellular Therapy for People With Central Nervous System Lymphoma (CNSL)

Inclusion Criteria: * Men and women who are at least 18 years of age on the day of consenting to the study. * Histologically documented primary or secondary central nervous system lymphoma of DLBCL subtype * Relapsed/refractory primary or secondary CNSL patients. All recurrent/refractory patients need to have received at least one prior CNS-directed methotrexate-based therapy. There is no restriction on the number of recurrences. * For recurrent/refractory patients, parenchymal lesions must have unequivocal evidence of disease progression on imaging (MRI of the brain or head CT) within 21 days of study consent. For patients with leptomeningeal disease only, CSF cytology and/or flow cytometry must document CSF findings consistent with CSF involvement by lymphoma and/or imaging findings consistent with CSF disease within 21 days of study registration (at the discretion of the investigator). * Creatinine Clearance ≥ 40 ml/min/m2, direct bilirubin ≤2.0 mg/100 ml, AST and ALT ≤3.0x upper limit of normal (ULN) * Adequate pulmonary function as assessed by ≥90% oxygen saturation on room air by pulse oximetry. * Must be able to tolerate both MRI and CT scans * Must be able to tolerate lumbar puncture and/or Ommaya taps * Must have been either off corticosteroids, or on a stable or decreasing dose of prednisone equivalent ≤ 10 mg daily for 7 days before apheresis and 72 hours prior to CAR T cell infusion o Use of corticosteroids to treat CAR T cell toxicities per MSKCC guidelines is permitted Exclusion Criteria: * ECOG performance status \>2 o Patients with ECOG status of 2 will be enrolled at the discretion of the PI * Active systemic lymphoma (i.e. involvement outside of the CNS) * If the most recent CSF or brain tissue sample demonstrates absence of CD19 expression * Size of any single CNS lymphoma lesion exceeds 3 cm in maximal diameter * Prior treatment of systemic lymphoma with CD19-targeted CAR T cells * Pregnant or lactating patients. Patients of childbearing age should use effective contraception while on this study and continue for 1 year after all treatment is finished. * Impaired cardiac function (LVEF \<40%) as assessed by most recent ECHO in the last 1 year. * Patients with autoimmune disease requiring systemic T cell-suppressive therapy. * Patients with following cardiac conditions will be excluded: * New York Heart Association (NYHA) stage III or IV congestive heart failure * Myocardial infarction ≤6 months prior to enrollment * History of clinically significant ventricular arrhythmia or unexplained syncope, not believed to be vasovagal in nature or due to dehydration ≤6 months prior to enrollment * Patients with ocular lymphoma in the absence of other CNS involvement * Patient has received chemotherapy, monoclonal antibodies or targeted anticancer therapy ≤ 4 weeks or 5 half-lives, whichever is shorter, or 6 weeks for nitrosourea or mitomycin-C, or 3 months since allogeneic hematopoietic stem cell transplantation, prior to starting the study drug, or the patient has not recovered from the side effects of such therapy. * Patients with HIV * Patients with active hepatitis B or hepatitis C infection (as manifested by either detectable hepatitis B virus DNA by PCR, hepatitis virus C RNA by PCR, or positivity for hepatitis B surface or core antigen) * Patients with uncontrolled systemic fungal, bacterial, viral or other infection at time of leukapheresis or at time of CAR T cell infusion * Patients with any concurrent active malignancies as defined by malignancies requiring any therapy other than expectant observation or hormonal therapy, with the exception of squamous and basal cell carcinoma of skin * Patients exposed to immune checkpoint inhibitor within 8 weeks * Use of herbal supplements are not allowed on study * Any other issue which, in the opinion of the treating physician or PI, would make the patient ineligible for the study.