Maintenance Obinutuzumab in Treating Patients With Central Nervous System Lymphoma Who Have Achieved a Complete or Partial Response

Inclusion Criteria: * CD20+ B-cell primary central nervous system lymphoma (PCNSL) confirmed at the time of diagnosis by histology, cytology, or immunocytochemistry from cerebrospinal fluid (CSF); diagnosis must be documented by pathology report. * Must have undergone first-line treatment with a high-dose methotrexate-based chemotherapy regimen with or without brain radiotherapy; high-dose methotrexate is defined as \>= 3 grams/m\^2; methotrexate dose reduction for creatinine clearance \< 100 ml/min is permitted * Must be within 75 days of completion of first-line treatment regimen at the time of randomization; must have achieved objective response (PR or CR/unconfirmed complete response \[CRu\]) to first-line treatment * Brain magnetic resonance imaging (MRI) documenting objective response must be obtained within 30 days before randomization * If CSF was positive for lymphoma cells at diagnosis or during first-line treatment and/or a slit lamp examination was positive at diagnosis or during first-line treatment, then the CSF and vitreal studies must have been repeated and must have indicated CR; Note: CR requires complete disappearance of all enhancing abnormalities on gadolinium-enhanced MRI; if CSF was positive for lymphoma cells at diagnosis or during first-line treatment and/or slit lamp examination was positive at diagnosis or during first-line treatment, then the CSF and vitreal studies must have been repeated and must have indicated CR; for CRu, some patients will have a small but persistent enhancing abnormality on MRI related to biopsy or focal hemorrhage; it is often difficult to ascertain whether this represents a residual nidus of tumor or scar tissue; if the abnormality does not change or slowly involutes without therapy and corticosteroids, it is reasonable to categorize as a CRu; at the time CR/CRu is determined, the patient should not have used corticosteroids for at least two weeks * Karnofsky performance status (KPS) \>= 60; Eastern Cooperative Oncology Group (ECOG) 0, 1, or 2 * Signed informed consent form (ICF) * Ability and willingness to comply with the requirements of the study protocol * Total bilirubin \< 3 x the upper limit of normal (ULN), ≤ 7 days before date of randomization * Creatinine clearance \> 30 mL/min (calculated according to institutional standards or using Cockcroft-Gault formula), ≤ 7 days before date of randomization * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≤ 5 x ULN, ≤7 days before date of randomization * Platelet ≤ 75,000 cells/mm\^3, ≤ 7 days before date of randomization * Hemoglobin \> 9 g/dL, ≤ 7 days before date of randomization * Absolute neutrophil count \> 1.5 x 10\^3 cells/mm\^3, ≤ 7 days before date of randomization * Surgically sterile or agree to use effective contraception using an adequate measure of contraception such as oral contraceptives, intrauterine device, or barrier method of contraception in conjunction with spermicidal jelly while receiving obinutuzumab and \>= 18 months after the last dose of obinutuzumab for women, and 180 days after the last dose of obinutuzumab for men Exclusion Criteria: * History of severe allergic or anaphylactic reactions to monoclonal antibody therapy * Clinical evidence of extra-central nervous system (CNS) (systemic) non-Hodgkin lymphoma * Known hypersensitivity to any of the study drugs * History of other malignancy that could affect compliance with the protocol or interpretation of results * Patients with a history of curatively treated basal or squamous cell carcinoma of the skin or in situ carcinoma of the cervix are generally eligible; patients with a malignancy that has been treated, but not with curative intent, will also be excluded, unless the malignancy has been in remission without treatment for \>= 2 years prior to randomization * Known active bacterial, viral, fungal, mycobacterial, or other infection (excluding fungal infections of nail beds) or any major episode of infection requiring treatment with IV antibiotics or hospitalization (related to the completion of the course of antibiotics) within 4 weeks prior to study randomization * Major surgery within 4 weeks prior to study randomization * Known infection with human immunodeficiency virus (HIV) * Positive hepatitis serologies: * Hepatitis B (HBV): patients with positive serology for hepatitis B defined as positivity for hepatitis B surface antigen (HBsAg) or hepatitis B core antibody (anti-HBc); patients who are positive for anti-HBc may be considered for inclusion in the study on a case-by-case basis if they are hepatitis B viral deoxyribonucleic acid (DNA) negative and are willing to undergo ongoing HBV DNA testing by real-time polymerase chain reaction (PCR); patients with positive serology may be referred to a hepatologist or gastroenterologist for appropriate monitoring and management * Hepatitis C (HCV): patients with positive hepatitis C serology unless HCV ribonucleic acid (RNA) is confirmed negative and may be considered for inclusion in the study on a case-by-case basis * Women who are pregnant or lactating * Vaccination with a live vaccine a minimum of 4 weeks prior to study randomization