Ofatumumab, Pentostatin, and Cyclophosphamide in Treating Patients With Untreated Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Diagnosis of CLL according to the National Cancer Institute (NCI) criteria or SLL according to the World Health Organization (WHO) criteria, including previous documentation of: * Biopsy-proven SLL * Diagnosis of CLL according to NCI working group criteria as evidenced by all of the following: * Peripheral blood lymphocyte count of \> 5,000/mm\^3 consisting of small to moderate size lymphocytes, with \< 55% prolymphocytes * Immunophenotyping 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 expression (typically dim immunoglobulin expression) * Note: splenomegaly, hepatomegaly, or lymphadenopathy are not required for the diagnosis of CLL * Before diagnosing CLL or SLL, mantle cell lymphoma must be excluded by demonstrating a negative FISH analysis for t(11;14)(immunoglobulin heavy \[IgH\]/cyclin D1 \[CCND1\]) on peripheral blood or tissue biopsy or negative immunohistochemical stains for CCND1 on involved tissue biopsy * Patients must be previously untreated and meet at least one of the following indications for chemotherapy: * Evidence of progressive marrow failure as manifested by the development of or worsening anemia (=\< 11 g/dl) and/or thrombocytopenia (=\< 100,000/mm\^3) not due to autoimmune disease * Symptomatic or progressive lymphadenopathy, splenomegaly or hepatomegaly * One or more of the following disease-related symptoms: * Weight loss \> 10% within the previous 6 months * Extreme fatigue attributed to CLL * Fevers \> 100.5 degree Fahrenheit for 2 weeks without evidence of infection * Drenching night sweats without evidence of infection * Progressive lymphocytosis due to CLL with an increase of \> 50% over a two-month period or an anticipated doubling time of less than six months * Prior chemotherapy or monoclonal antibody based therapy for treatment of CLL will be considered prior therapy; nutraceutical treatments with no established benefit in CLL (such as epigallocatechin gallate \[EGCG\], found in green tea or other herbal treatments) will not be considered "prior treatment" * Marked hypogammaglobulinemia or the development of a monoclonal protein in the absence of any of the above criteria for active disease are not sufficient for protocol therapy * Serum creatinine =\< 1.5 x upper normal levels (UNL) * Total bilirubin =\< 1.5 x UNL unless due to Gilbert's disease; if total bilirubin is \> 1.5 x UNL, a direct bilirubin should be performed and must be \< 1.5 mg/dL for Gilbert's to be diagnosed * Aspartate aminotransferase (AST) =\< 3.0 x UNL and alanine aminotransferase (ALT) =\< 3.0 x UNL (unless due to hemolysis or CLL) * Eastern Cooperative Oncology Group (ECOG) performance status (PS): 0, 1, or 2 * Willingness to provide blood samples as required * Able to adhere to the study visit schedule and other protocol requirements Exclusion Criteria: * Any of the following comorbid conditions: * New York Heart Association Class III or IV heart disease * Recent myocardial infarction (\< 1 month) * Uncontrolled infection * Infection with the human immunodeficiency virus (HIV/acquired immunodeficiency syndrome \[AIDS\]) * Infection with known chronic, active Hepatitis C * Positive serology for hepatitis B (HB) defined as a positive test for HB surface antigen (HBsAg); in addition, if negative for HBsAg but HB core antibody (HBcAb) positive (regardless of HBsAb status), a HB deoxyribonucleic acid (DNA) test will be performed and if positive the subject will be excluded * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Other active primary malignancy requiring treatment or limiting survival to =\< 2 years * Any radiation therapy =\< 4 weeks prior to registration * Any major surgery =\< 4 weeks prior to registration * 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 conditions; Note: previous use of corticosteroids is allowed * 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