• 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 in the CLL-IPI are unknown including IGVH mutation status results not being available due to a failed laboratory assay, the patient is not eligible

⁃ Note: When determining CLL-IPI, use most recent test results, if more than one result is available

⁃ Note: Patients with CLL-IPI risk category of high risk or very high risk (total score of 4-10) will be randomized to Arms A or B

⁃ Note: Patients with CLL-IPI risk category of low risk or intermediate risk (total score of 0-3) will be registered to Arm C

• Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, or 2

• Provide written informed consent

• Willing to provide blood and saliva samples for correlative research purposes

• Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Absolute neutrophil count (ANC) \>= 1500/mm\^3 (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Platelet count \>= 100,000/mm\^3 (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Hemoglobin \>= 11.0 g/dL (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Aspartate aminotransferase (aspartate transaminase \[AST\]) =\< 3 x upper limit of normal (ULN) (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Creatinine =\< 1.5 X ULN (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Total bilirubin =\< 1.5 x upper limit of normal (ULN) (or total bilirubin =\< 3.0 x ULN with direct bilirubin =\< 1.5 x ULN in patients with well-documented Gilbert's syndrome (obtained =\< 30 days prior to randomization)

• For high risk and very high risk CLL-IPI (Arms A and B) only: Prothrombin time (PT), international normalized ratio (INR), and partial thromboplastin time (PTT) =\< 1.5 X ULN OR if patient is receiving anticoagulant therapy and PT or PTT is within therapeutic range of intended use of coagulants (obtained =\< 30 days prior to randomization)

• Negative serum pregnancy test done =\< 7 days prior to registration, for persons of childbearing potential only

• Will provide bone marrow aspirate sample for correlative research purposes