Ibrutinib and Rituximab Compared With Fludarabine Phosphate, Cyclophosphamide, and Rituximab in Treating Patients With Untreated Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Diagnosis of CLL according to the National Cancer Institute (NCI)/Internal 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 x 10\^9/L * Immunophenotype consistent with CLL defined as: * The predominant population of lymphocytes share both B-cell antigens (cluster of differentiation \[CD\]19, 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 FISH analysis for t(11;14)(immunoglobulin heavy locus \[IgH\]/cyclin D1 \[CCND1\]) 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, Bruton's tyrosine kinase (BTK) inhibitor therapy, 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 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 * ECOG performance status between 0-2 * Life expectancy of \>= 12 months * Ability to tolerate FCR based therapy * 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 =\< 2.5 x upper limit of normal (ULN) (obtained =\< 14 days prior to registration) unless due to Gilbert's disease; for those with a total bilirubin \> 2.5 x ULN, a direct bilirubin should be performed and must be \< 1.5 mg/dL for Gilbert's to be diagnosed * If value is higher due to hepatic involvement by CLL, patient is eligible * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate transaminase \[AST\])/serum glutamate-pyruvate transaminase (SGPT) (alanine transaminase \[ALT\]) =\< 3.0 x the institutional ULN (obtained =\< 14 days prior to registration) * 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) * If value is higher due to hepatic involvement by CLL, patient is eligible * 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) used for treatment of non-hematologic medical condition (e.g. chronic adrenal insufficiency) is permitted * No previous use of corticosteroids for autoimmune complications that have developed since the initial diagnosis of CLL; 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, they must not 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 the last 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 * Patients with human immunodeficiency virus (HIV) infection may be eligible provided they meet the following criteria: * CD4-positive cell count \>= lower limit of institutional normal * HIV viral load \< 10,000 copies HIV ribonucleic acid (RNA)/mL (if not on anti-HIV therapy) OR \< 50 copies HIV RNA/mL (if on anti-HIV therapy) * No evidence of hepatitis B or C infection * No evidence of resistant strains of HIV * No history of acquired immune deficiency syndrome (AIDS)-defining condition * 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 * Serologic status reflecting active hepatitis B or C infection; patients that are positive for hepatitis B core antibody, hepatitis B surface antigen (HBsAg), or hepatitis C antibody must have a negative polymerase chain reaction (PCR) prior to enrollment (PCR positive patients will be excluded) * Patients are not eligible if they require treatment with a strong cytochrome P450 (CYP) family 3, subfamily A (3A) inhibitor * 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 an investigational agent whose genotoxic, mutagenic, and teratogenic effects on the developing fetus and newborn are unknown; female patients of childbearing potential must have a negative serum pregnancy test within 2 weeks prior to registration to rule out pregnancy; female patients who are of non-reproductive potential are those who are post-menopausal by history (i.e. no menses for \>= 1 year); OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy) * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception or to abstain from sexual intercourse for 90 days after the last dose of study drug * 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)