Obinutuzumab and Ibrutinib as Front Line Therapy in Treating Patients With Indolent Non-Hodgkin's Lymphomas

Inclusion Criteria: * Previously untreated, histologically confirmed indolent non-Hodgkin's lymphoma as follows: * Follicular lymphoma (World Health Organization \[WHO\] classification grade 1, 2, or 3a) * Marginal zone lymphoma including: * Nodal and splenic marginal zone lymphoma (MZL) who have an indication for systemic therapy * Extranodal MZL: * Nongastric/noncutaneous MZL requiring systemic therapy * Cutaneous MZL will be eligible only if they have pathologically confirmed extra-cutaneous disease * Gastric MZL only if stage IIIE/IV defined as lymph node involvement on both sides of the diaphragm or with disseminated extranodal disease such as bone marrow or additional extra nodal sites * Pathological diagnosis should be obtained by incisional or excisional tissue biopsy; core biopsy is permissible if obtaining an incisional or excisional is not possible and if the grade can be assessed on the core biopsy; a core biopsy can also be used if deemed in the best interest of the patient in the opinion of the investigator * Patients must have stage II-IV disease * All patients should have measurable disease; measurable disease is defined as a lymph node or tumor mass that is \>= 1.5 cm in at least one dimension by computed tomography (CT) or the CT portion of the PET/CT * Documentation of CD20+ status * Patients must have an indication for therapy per standard modified Groupe d'Etude des Lymphomes Folliculaires (GELF) criteria including: * Symptoms attributable to lymphoma * B symptoms * Threatened end-organ function * Pleural effusions or peritoneal ascites * Cytopenia secondary to lymphoma * Leukemia * Bulky disease (defined as: Single mass \>7cm in diameter, or 3 or more masses \> 3 cm in diameter) * Splenomegaly * And steady progression over at least 6 months * Age \> 18 years * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Patients must be able to swallow whole pills * Ability and willingness to comply with the requirements of the study protocol; when it is determined by the study investigator that a potential research participant is cognitively impaired, a surrogate consent from a caregiver or legally-authorized representative will be obtained. Caregiver or legally-authorized representative will ensure that they comply with the protocol in order for the subject to be considered eligible * Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy); female subjects of childbearing potential must have a negative urine/serum pregnancy test upon study entry * Male and female subjects who agree to use both a highly effective method of birth control (e.g., implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], complete abstinence , or sterilized partner) and a barrier method (e.g., condoms, vaginal ring, sponge, etc) during the period of therapy; female patients of reproductive potential who are not surgically sterile must practice adequate birth control for a minimum of twelve months post-treatment; male patients who are not surgically sterile must practice adequate birth control for a minimum of three months post-treatment * Absolute neutrophil count \> 1.5 x 10\^9 cells/mm\^3 * Platelet count \> 50,000 cells/mm\^3 (50 x 10\^9/L) * Hemoglobin \> 9.0 g/dL * Serum aspartate transaminase or alanine transaminase =\< 3.0 x upper limit of normal (ULN) * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 x ULN and activated partial thromboplastin time (aPTT) \< 1.5 x ULN (unless abnormalities are unrelated to coagulopathy or bleeding disorder) * Estimated creatinine clearance \>= 30 ml/min (calculated according using Cockcroft-Gault formula) * Bilirubin =\< 1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * Patients with Child Pugh B or C liver failure will be excluded Exclusion Criteria: * Prior history of malignancies unless the patient has been disease free for \>= 5 years; exceptions include basal cell carcinoma or squamous cell carcinoma of the skin; carcinoma in situ of cervix; carcinoma in situ of breast, localized prostate cancer, or superficial bladder cancer that has undergone curative therapy * Prior therapy for lymphoma including chemotherapy or immunotherapy including ibrutinib/anti-CD20 agents; patient may have received corticosteroids, but should be off them 2 weeks prior to study entry; known prior significant hypersensitivity to obinutuzumab (not including infusion reactions) or ibrutinib * Patients with evidence of large B cell transformation (transformed disease) are not eligible * Known central nervous system (CNS) involvement by lymphoma * Known bleeding disorders (e.g., von Willebrand's disease or hemophilia) * Concomitant use of warfarin or other vitamin K antagonists * Requires treatment with a strong cytochrome P450 (CYP) 3A inhibitor * 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 before the start of cycle 1 * Known infection with human immunodeficiency virus (HIV) or human T-cell leukemia virus 1 (HTLV-1) seropositive status * Viral hepatitis: * Patients with active hepatitis B defined by hepatitis B surface antigen positivity or core antibody positivity in the presence of detectable serum hepatitis B deoxyribonucleic acid (DNA) viremia are not eligible for this study * Patients with a positive hepatitis B core antibody but with negative hepatitis B DNA maybe considered for participation, but must agree to receive appropriate anti-hepatitis B viral therapy suppression therapy while on obinutuzumab and have hepatitis B DNA monitored every 4 weeks with real-time polymerase chain reaction (PCR) by the treating physician; these patients should be referred to a hepatologist or gastroenterologist for appropriate monitoring and management * Hepatitis C: patients with positive hepatitis C serology unless hepatitis C virus (HCV) ribonucleic acid (RNA) is confirmed negative by PCR * Vaccination with a live vaccine a minimum of 28 days prior to the start of treatment * Patient is receiving other investigational drugs * Prior chemotherapy for any other cancer within the last 2 years * Patients should not have active or uncontrolled autoimmune hemolytic anemia or immune thrombocytopenia * Patients should not have transfusion-dependent thrombocytopenia or bleeding disorders * Patients should not have an autoimmune disorder that requires active immunosuppression * Patients should not have a history of uncontrolled seizures * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or class 3 or 4 congestive heart failure as defined by the New York Heart Association functional classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to enrollment on the study * Patients should not have a stroke or intracranial hemorrhage within last 6 months * Prior surgery: patients may not have had major surgery within 28 days of enrollment, or minor surgery within 7 days of enrollment; examples of minor surgery include dental surgery, insertion of a venous access device, skin biopsy, or aspiration of a joint; the decision about whether a surgery is major or minor can be made at the discretion of the treating physician * Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * Pregnant and nursing: female patients must have a negative serum pregnancy test within 72 hours prior to initiating protocol therapy and be practicing an effective form of contraception during protocol therapy and for at least 4 weeks following completion of protocol therapy * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification