Intracerebroventricular Administration of CD19-CAR T Cells (CD19CAR-CD28-CD3zeta-EGFRt-expressing Tcm-enriched T-lymphocytes) for the Treatment of Primary Central Nervous System Lymphoma

Inclusion Criteria: Participant must have the ability to understand and the willingness to sign a written informed consent Note: For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent is processed. However, the research participant can proceed with lymphodepletion (if applicable) and CAR T cell infusion only after the translated full consent form is signed Agreement to allow the use of archival tissue from diagnostic tumor biopsies. If unavailable exceptions may be granted with study principal investigator (PI) approval Age >= 18 years Eastern Cooperative Oncology Group (ECOG) performance status 0 - 2 Documented primary CNS lymphoma. Progression must be determined radiographically. Participant must have measurable disease which could be a measurable lymphomatous mass or, in the case of leptomeningeal only disease, measurable lymphoma cells in CSF by flow cytometry Documented current CD19+ tumor expression if prior CD19 directed therapy was used Participant must have received and failed or have been intolerant to CNS directed therapy like high dose methotrexate or high dose cytarabine based regimens. Participants are not required to have failed all of these agents if, in the investigator's opinion, they would benefit from treatment on the current protocol No known contraindications to leukapheresis, steroids or tocilizumab Participant of reproductive potential must agree to use acceptable birth control methods throughout study therapy and for 3 months after final dose of study treatment Total serum bilirubin =< 2.0 mg/dL (within 14 days of signing the screening and leukapheresis consent) Patients with Gilbert syndrome may be included if their total bilirubin is =< 3.0 x upper limit of normal (ULN) and direct bilirubin =< 1.5 x ULN Aspartate aminotransferase (AST) =< 2.5 x ULN (within 14 days of signing the screening and leukapheresis consent) Alanine aminotransferase (ALT) =< 2.5 x ULN (within 14 days of signing the screening and leukapheresis consent) Creatinine clearance of >= 50 mL/min per the Cockcroft-Gault formula (within 14 days of signing the screening and leukapheresis consent) Cardiac function (12 lead-electrocardiogram [ECG]) without acute abnormalities requiring investigation or intervention (within 14 days of signing the screening and leukapheresis consent) Absolute neutrophil count >= 750/uL (within 14 days of signing the screening and leukapheresis consent) Hemoglobin (Hb) >= 8 g/dl (within 14 days of signing the screening and leukapheresis consent) Platelet count >= 50,000/uL (within 14 days of signing the screening and leukapheresis consent) Ejection fraction measured by echocardiogram or multigated acquisition scan (MUGA) > 40% (evaluation within 6 weeks of screening does not need to be repeated) (within 14 days of signing the screening and leukapheresis consent) Oxygen (O2) saturation > 92% not requiring oxygen supplementation (within 14 days of signing the screening and leukapheresis consent) Women of childbearing potential (WOCBP): negative urine or serum pregnancy test (within 14 days of signing the screening and leukapheresis consent) If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required Exclusion Criteria: Participants who received prior CAR T cell therapy Participant has not yet recovered from toxicities of prior therapy Participant with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of signing the screening and leukapheresis consent Participant with known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system, including seizure disorder Active autoimmune disease requiring systemic immunosuppressive therapy Needing dexamethasone more than 4mg/day (or equivalent) within 72 hours prior to leukapheresis or CAR T cell infusion History of allergic reactions attributed to compounds of similar chemical or biologic composition or other agents used in this study Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia History of stroke or intracranial hemorrhage within 6 months prior to signing the screening and leukapheresis consent History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent with no known active disease present for >= 3 years, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin Uncontrolled active infection Active hepatitis B or hepatitis C infection: subjects who are hepatitis B core antibody (anti-HBc) positive and who are surface antigen negative will need to have a negative polymerase chain reaction (PCR) result. Those who are hepatitis B surface antigen (HbsAg) positive or hepatitis B PCR positive will be excluded Subjects who are hepatitis B core antibody positive (or have a known history of hepatitis B virus [HBV] infection) should be monitored quarterly with a quantitative PCR test for HBV deoxyribonucleic acid (DNA). HBV monitoring should last until 12 months after last dose of study drug. Any subject with a rising viral load (above lower limit of detection) should discontinue study drug and have antiviral therapy instituted and a consultation with a physician with expertise in managing hepatitis B. Subjects who are core antibody (Ab) positive at study enrollment are strongly recommended to start Entecavir before start and until completion of study treatment Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded Subjects who are hepatitis C antibody positive will need to have a negative PCR result. Those who are hepatitis C PCR positive will be excluded Human immunodeficiency virus (HIV) infection Active significant bacterial, fungal or viral (other than those listed) infections Any other condition that would, in the investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns with clinical study procedures Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)