Obinutuzumab in Combination With Ibrutinib in Treating Patients With Relapsed Mantle Cell Lymphoma

Inclusion Criteria: * Subjects must have a diagnosis of relapsed or refractory mantle cell lymphoma as follows: * Diagnosis of mantle cell lymphoma (MCL) must include morphology and expression of either cyclin D1 in association with other relevant markers (eg, CD19, CD20, CD5) or evidence of t(11;14) as assessed by cytogenetics, fluorescent in situ hybridization (FISH), or polymerase chain reaction (PCR) * Relapsed or refractory disease is defined as no response or progressive disease to prior treatment if the prior treatment comprised any of the following: * 1 regimen containing an anti-CD20 antibody administered for \>= 2 doses, and/or * \>= 1 regimen containing 1 cytotoxic agent (e.g., bendamustine, chlorambucil, cyclophosphamide, cytarabine, doxorubicin) administered for 2 cycles * At least 1 measurable site of disease according to Revised Response Criteria for Malignant Lymphoma (Cheson Criteria); the site of disease must be greater than 1.5 cm in the long axis regardless of short axis measurement or greater than 1.0 cm in the short axis regardless of long axis measurement, and clearly measurable in 2 perpendicular dimensions * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Absolute neutrophil count (ANC) \>= 1.0 K/cu mm; for subjects with ANC \< 1.0 K/cu mm due to significant marrow involvement by MCL, ANC must be \> .5 K/cu mm * Platelets (plt) \>= 50 K/cu mm; for subjects with plt \< 50 K/cu mm due to significant marrow involvement by MCL, plt must be \> 25 K/cu mm * Total bilirubin =\< 2.5 X institutional limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal * Creatinine =\< 2 * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials; men must agree to not donate sperm during and after the study; for females, these restrictions apply for 18 months after last dose of obinutuzumab, or 1 month after the last dose of ibrutinib, whichever is later; for males, these restrictions apply for 180 days after the last dose of obinutuzumab or 3 months after the last dose of ibrutinib, whichever is later * Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[beta-hCG\]) or urine pregnancy test at screening; women who are pregnant or breastfeeding are ineligible for this study * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Major surgery within 4 weeks of drug administration * Diagnosed or treated for malignancy other than MCL, except: * Malignancy treated with curative intent and with no known active disease present for \>= 2 years * Adequately treated non-melanoma skin cancer or melanoma in situ without evidence of disease * Adequately treated cervical carcinoma in situ without evidence of disease * Asymptomatic prostate cancer managed with "active surveillance" * Localized prostate cancer treated with definitive treatment including radiation or surgery. Patients on adjuvant hormone deprivation treatment such as lupron are eligible. Patients with known metastatic disease are ineligible * History of stroke or intracranial hemorrhage within 6 months prior to randomization * Requires anticoagulation with warfarin or equivalent vitamin K antagonists (eg, phenprocoumon) * Vaccinated with live, attenuated vaccines within 4 weeks of randomization * Requires treatment with strong cytochrome P450 3A (CYP3A) inhibitors * Subjects who have had standard cytotoxic chemotherapy or radiotherapy within 3 weeks prior to entering the study or those whose adverse events due to agents administered more than 3 weeks earlier have not recovered to =\< grade 1; this excludes alopecia and hematologic adverse events * Subjects who have had radiotherapy within 2 weeks prior to entering the study or those whose adverse events due to radiotherapy more than 2 weeks earlier have not recovered to =\< grade 1 * Subjects who have received investigational or approved oral or "targeted" agents (such as spleen tyrosine kinase \[SYK\], phosphatidylinositol 3 kinase \[PI3K\], B-cell chronic lymphocytic leukemia \[CLL\]/lymphoma 2 \[bcl-2\], BTK inhibitors) or lenalidomide within 1 week prior to entering the study or those whose adverse events due to agents administered more than 1 week earlier have not recovered to =\< grade 1; this excludes hematologic adverse events; the exception is subjects who are currently receiving ibrutinib (for \< 14 days). In this case, ibrutinib can be continued * Subjects who have received monoclonal antibodies (such as Rituxan) within 1 week prior to entering the study or those whose adverse events due to agents administered more than 1 week earlier have not recovered to =\< grade 1; this excludes hematologic adverse events * Subjects who are actively receiving any other investigational agents * History of severe allergic reactions attributed to compounds of similar chemical or biologic composition as obinutuzumab or ibrutinib or other agents used in the study * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or lactating women are excluded from this study * Known history of human immunodeficiency virus (HIV) or active hepatitis C * Virus or active hepatitis B virus infection; patients who are hepatitis B core antibody (HBcAb) positive may be eligible as long as there is no evidence of active infection with negative hepatitis B (Hep B) by polymerase chain reaction (PCR); in this case, Hep B PCR must be monitored monthly * Any uncontrolled active systemic infection requiring intravenous (IV) antibiotics * Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib capsules, or put the study outcomes at undue risk * Patients previously treated with ibrutinib \> 14 days are ineligible; no drug intervention or cessation is required for patients already receiving ibrutinib prior to initiation of on-study therapy * Active graft versus (vs.) host disease (GVHD) * Ongoing glucocorticoids (prednisone \> 10 mg daily, or equivalent); higher doses (\> 10 mg daily) are permitted for up to 5 days to help control disease related symptoms