Acalabrutinib With or Without Obinutuzumab in Treating Patients With Early-Stage Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Age \>= 18 years * Diagnosis of: * Biopsy-proven small lymphocytic lymphoma (SLL) , or * Diagnosis of chronic lymphocytic leukemia (CLL) with a clonal B-cell population in the peripheral blood with immunophenotyping consistent with CLL as follows: * The 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) or other genetic method (e.g. IGHV analysis) * Before diagnosing CLL or SLL, mantle cell lymphoma must be excluded by demonstrating a negative fluorescence in situ hybridization (FISH) analysis for t(11;14)(IgH/CCND1) * Patients must be previously untreated * Note: Prior chemotherapy or monoclonal antibody based therapy for treatment of CLL or SLL will be considered prior therapy; nutraceutical treatments with no established benefit in CLL (such as epigallocatechin gallate or EGCG, found in green tea or other herbal treatments or supplemental vitamins) will not be considered "prior treatment"; prior corticosteroid therapy for an indication other than CLL/SLL will not be considered "prior treatment" * All patients will undergo testing for prognostic factors according to the CLL-IPI (testing obtained =\< 730 days prior to registration) * Note: If the results for any of the prognostic factors included…