Methotrexate, Mannitol, Rituximab, and Carboplatin in Treating Patients With Newly Diagnosed Primary Central Nervous System Lymphoma

Inclusion Criteria: * Subjects with histopathologic confirmation of intermediate or high-grade primary central nervous system lymphoma (PCNSL) as documented by brain biopsy, or cytology (analysis from cerebral spinal fluid \[CSF\] or vitrectomy), and cluster of differentiation 20 (CD20) positive; whenever possible, the tumor should be characterized by immunophenotype * Subjects must be =\< 90 days from diagnosis of PCNSL in the brain or spine; time from pathologic diagnosis to initiation of treatment should be specified; subjects with history of only ocular lymphoma are eligible if \< 90 days since documented brain parenchymal disease (by imaging or by biopsy) * Subjects must have an Eastern Cooperative Oncology Group (ECOG) performance score =\< 3 (Karnofsky \>= 30) * Hematocrit \>= 25% (may be reached by transfusion) (performed within 14 days of registration) * White blood cell count \>= 2.5 x 10\^3/mm\^3 (performed within 14 days of registration) * Absolute granulocyte count \>= 1.2 x 10\^3/mm\^3 (performed within 14 days of registration) * Platelets \>= 100 x 10\^3/mm\^3 (or \>= lower limit of institutional normal value) (performed within 14 days of registration) * Calculated creatinine clearance (Cr Cl) \>= 50 ml/min (performed within 14 days of registration); eligible for full dose methotrexate * Calculated Cr Cl \>= 30 ml/min (performed within 14 days of registration); eligible for reduced dose methotrexate * Bilirubin =\< 2.0 x upper limit of institutional normal value (performed within 14 days of registration) * The subject may have had other systemic chemotherapy for PCNSL during the 90 days since PCNSL diagnosis; prior systemic chemotherapy must have been given at least 4 weeks prior to study entry (6 weeks for nitrosourea agents), with the exceptions of methotrexate and rituximab which may have been given at least 10 days prior; ocular lymphoma treatment may have been given any time prior to study entry; if the subject has undergone treatment for parenchymal disease and the parenchymal disease has progressed on a stable or increasing dose of steroids, the subject is not eligible for enrollment * Sexually active women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study treatment and for the duration of study treatment; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Subjects with a bone marrow biopsy which shows microscopic, low-level involvement of lymphoma are eligible * Subject with seropositivity for hepatitis B or hepatitis C must be cleared by hepatology service prior to participating in treatment protocol Exclusion Criteria: * Prior cranial or spinal radiotherapy * Subjects with radiographic signs of excessive intra-cranial mass effect with associated rapid neurologic deterioration, and/or spinal block, are unsafe to undergo BBBD chemotherapy and are not eligible * Uncontrolled (over the last 30 days), clinically significant confounding medical conditions * Seropositivity for the human immunodeficiency virus * Systemic lymphoma * Subjects who have a positive serum human chorionic gonadotropin (hCG), are pregnant or lactating are ineligible * Known allergy to any of the study agents * Subjects who are at significant risk for general anesthesia