Assessing the Ability of Combination Treatment With Venetoclax to Permit Time Limited Therapy in Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of CLL according to the National Cancer Institute (NCI)/International Workshop on Chronic Lymphocytic Leukemia (IWCLL) criteria or small lymphocytic lymphoma (SLL) according to the World Health Organization (WHO) criteria. This includes previous documentation of: * Biopsy-proven small lymphocytic lymphoma OR * Diagnosis of CLL according to the NCI/IWCLL criteria as evidenced by all of the following: * Peripheral blood lymphocyte count of greater than 5 x10\^9/L * Immunophenotype consistent with CLL defined as: * The predominant population of lymphocytes share both B-cell antigens (CD19, CD20 \[typically dim expression\], or CD23) as well as CD5 in the absence of other pan-T-cell markers (CD3, CD2, etc). * Clonality as evidenced by kappa or lambda light chain restriction (typically dim immunoglobulin expression) * Negative fluorescent in situ hybridization (FISH) analysis for t(11;14)(IgH/CCND1) on peripheral blood or tissue biopsy (e.g. marrow aspirate) or negative immunohistochemical stains for cyclin D1 staining on involved tissue biopsy (e.g. marrow aspirate or lymph node biopsy) * No prior chemotherapy, BTK inhibitor therapy, venetoclax, small molecule signaling inhibitor, or monoclonal anti-body therapy for treatment of CLL or SLL * Has met at least one of the following indications for treatment: * Evidence of progressive marrow failure as manifested by the development of worsening anemia (hemoglobin \[Hg\] \< 11 g/dl) and/or thrombocytopenia (platelets \< 100 x 10\^9/L) * Symptomatic or progressive lymphadenopathy, splenomegaly, or hepatomegaly * One or more of the following disease-related symptoms: * Weight loss \>= 10% within the previous 6 months * Grade 2 or 3 fatigue attributed to CLL * Fevers \> 100.5 degree Fahrenheit (F) for 2 weeks without evidence of infection * Clinically significant night sweats without evidence of infection * Progressive lymphocytosis (not due to the effects of corticosteroids) with an increase of \> 50% over a two-month period or an anticipated doubling time of less than six months * Age \>= 18 years and \< 70 * Eastern Cooperative Oncology Group (ECOG) performance status between 0-2 * Life expectancy of \>= 12 months * No deletion of 17p13 on cytogenetic analysis by FISH * Glomerular filtration rate (GFR) \> 40 mL/minute as calculated by the Cockcroft-Gault Formula (obtained =\< 14 days prior to registration) * Total bilirubin =\< 1.5 x upper limit of normal (ULN) unless due to Gilbert's disease. For those with a total bilirubin \> 1.5 x ULN, a direct bilirubin should be performed and must be \< 1.5 mg/dL for Gilbert's to be diagnosed (obtained =\< 14 days prior to registration) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\])/serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3.0 x the institutional ULN (obtained =\< 14 days prior to registration) * NOTE: If value is higher due to hepatic involvement by CLL, patient is eligible * Prothrombin time (PT)/international normalized ratio (INR) \< 1.5 ULN and partial thromboplastin time (PTT) (activated partial thromboplastin time \[aPTT\]) \< 1.5 x ULN (obtained =\< 14 days prior to registration) * No active hemolytic anemia requiring immunosuppressive therapy or other pharmacologic treatment. Patients who have a positive Coombs test but no evidence of hemolysis are NOT excluded from participation * No current use of corticosteroids. EXCEPTION: Low doses of steroids (\< 10 mg of prednisone or equivalent dose of other steroid; inhaled steroids) used for treatment of non-hematologic medical condition (e.g. chronic adrenal insufficiency) is permitted * No previous autoimmune complications (e.g. autoimmune hemolytic anemia or immune thrombocytopenia) that have developed since the initial diagnosis of CLL and have required treatment with high dose corticosteroids (e.g. equivalent of \> 20 mg/day of prednisone), monoclonal antibody based therapy, or chemotherapy. Prior use of corticosteroids for reasons other than treatment of autoimmune complications is allowed * No other active primary malignancy (other than non-melanomatous skin cancer or carcinoma in situ of the cervix) requiring treatment or limiting expected survival to =\< 2 years * NOTE: If there is a history of prior malignancy, the patient must not currently be receiving other specific treatment (other than hormonal therapy for their cancer) * Able to adhere to the study visit schedule and other protocol requirements * No major surgery within 4 weeks (28 days) of first dose of study drug or minor surgery within 3 days of first dose of study drug * No radiation therapy =\< 4 weeks prior to registration to Step 1 * Patients who are human immunodeficiency virus positive (HIV+) with undetectable HIV viral load are eligible provided they meet all other protocol criteria for participation and are not being treated with protease inhibitors or any non-nucleoside reverse transcriptase inhibitors (NNRTI) that are CYP3A4 inducers; if being treated for HIV, patients should be receiving an alternative antiretroviral therapy (ART) that is not a CYP3A inhibitor * Patients must not have any of the following conditions: * Congestive heart failure or New York Heart Association Functional Classification III or IV congestive heart failure * History of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to registration * Recent infections requiring systemic treatment; need to have completed anti-biotic therapy \> 14 days before the first dose of study drug * Cerebral vascular accident or intracranial bleed within the last 6 months * Infection with known chronic, active hepatitis C * Positive serology for hepatitis B defined as a positive test for hepatitis B surface antigen (HBsAg); in addition, if negative for HBsAg but hepatitis B core antibody (HBcAb) positive (regardless of hepatitis B surface antibody \[HBsAb\] status), a hepatitis B deoxyribonucleic acid (DNA) test will be performed and, if positive the subject will be ineligible; if the hepatitis (Hep) B DNA test is negative (i.e. viral load undetectable) then the individual is eligible; if a patient who is HBsAg negative, HBsAb negative, HBcAb positive, and Hep B DNA negative is enrolled, they should be considered for either prophylactic anti-viral therapy (J Clin Oncol. 2013 Aug 1;31(22):2765-72) or careful monitoring for Hep B reactivation (J Clin Oncol. 2014 Nov 20;32(33):3736-43) * Patients are not eligible if they require treatment with a strong cytochrome P450 (CYP) 3A inhibitor * Patients may not have received the following within 7 days prior to the first dose of study drug: * Steroid therapy for anti-neoplastic intent * Strong and moderate CYP3A inhibitors * Strong and moderate CYP3A inducers * Patients may not be on any other investigational agents * Patients may not have received warfarin or another vitamin K antagonist in the preceding 30 days * Women must not be pregnant or breast-feeding since this study involves investigational agents whose genotoxic, mutagenic, and teratogenic effects on the developing fetus and newborn are unknown. * All females of childbearing potential must have a blood test within 2 weeks prior to registration to Step 1 to rule out pregnancy. A patient of childbearing potential someone, regardless of whether they have undergone tubal ligation, who meets the following criteria: 1) has achieved menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal (amenorrhea following cancer therapy does not rule out childbearing potential) for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Women of childbearing potential and sexually active males must be strongly advised to use accepted and highly effective method(s) of contraception or to abstain from sexual intercourse for the duration of their participation in the study and for: * 18 months after the last dose of obinutuzumab * 90 days after the last dose of ibrutinib, and * 30 days after the last dose of venetoclax Male subjects must also agree to refrain from sperm donation until 90 days after the last dose of protocol treatment * Patient must be able to swallow capsules and not have the following conditions: * Disease significantly affecting gastrointestinal function * Resection of the stomach or small bowel * Symptomatic inflammatory bowel disease * Ulcerative colitis * Partial or complete bowel obstruction * Patient must not be on any other systemic immunosuppressant therapy other than corticosteroids within 28 days of the first dose of study drug * Patient must not be vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Patient must not have any known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * Patient must not have currently active, clinically significant hepatic impairment (\>= moderate hepatic impairment according to the NCI/Child Pugh classification) * Patient must undergo assessment with Timed Up and Go (TUG) test and comorbidity index * Patient must be able to receive xanthine oxidase inhibitor or rasburicase for tumor lysis syndrome (TLS) prophylaxis