Lenalidomide and Vaccine Therapy in Treating Patients With Early-Stage Asymptomatic Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria:

* Patients must have histologically identified chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL) as defined by the World Health Organization (WHO) classification of hematopoietic neoplasms
* CLL/SLL cells must demonstrate one or more of the following high-risk genomic features:

  * Deletion (Del) (17p13.1) as detected by fluorescence in-situ hybridization (FISH) in \> 20% of cells
  * Del(11q22.3) as detected by FISH in \> 20% of cells
  * Complex karyotype (\>= 3 cytogenetic abnormalities on stimulated karyotype)
  * Unmutated immunoglobulin variable heavy chain (IgVH) (\>= 98% sequence homology compared with germline sequence)
* Patients cannot meet any of the following consensus criteria for initiating treatment:

  * Progressive splenomegaly and/or lymphadenopathy identified by physical examination or radiographic studies
  * Progressive lymphocytosis with total white blood cell (WBC) \>= 300,000/uL
  * Anemia (\< 11 g/dL) or thrombocytopenia (\< 100,000/uL) due to bone marrow involvement
  * Presence of unintentional weight loss \> 10% over the preceding 6 months
  * National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or 3 fatigue
  * Fevers \> 100.5 degrees or night sweats for \> 2 weeks without evidence of infection
  * Progressive lymphocytosis with an increase of \> 50% over a 2 month period or an anticipated doubling time of \< 6 months
* No prior therapy for CLL/SLL, including chemotherapy, radiotherapy, and/or immunotherapy will be allowed
* Age ≥ 18 years and \< 80 years (or with justification if older than 80 years due to the higher risk of toxicity in patients older than 80 years). CLL is rare in children and likely represents a different disease process. As a result, children are excluded from this study but may be eligible for future pediatric phase 2 combination trials
* Estimated life expectancy of greater than 24 months
* Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)
* Total bilirubin =\< 1.5 times upper limit of normal (ULN) (unless secondary to Gilbert disease)
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate-pyruvate transaminase \[SGPT\]) =\< 2.5 times ULN
* Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal according to the Cockcroft-Gault formula
* Absolute neutrophil count (ANC) \>= 1,500/uL
* Platelet count \>= 100,000/uL
* Able to swallow capsules without difficulty and no history of malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction
* Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting lenalidomide. Further, they must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control: one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before starting lenalidomide. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP, even if they have had a successful vasectomy; a FCBP is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure

Exclusion Criteria:

* Patients who have had any treatment for their CLL/SLL, including but not limited to chemotherapy, radiotherapy, or immunotherapy, prior to entering the study
* No corticosteroid use will be permitted within two weeks prior to study, except for maintenance therapy for a non-malignant disease; maintenance therapy dose may not exceed 20 mg/day prednisone or equivalent
* Patients who meet consensus criteria for the treatment of CLL/SLL
* Patients may not be receiving any other investigational agents
* Patients with a recent history (within 6 months of study entry) of deep vein thrombosis (DVT)/pulmonary embolism (PE) are not eligible; patients with a distant history (greater than 6 months before study entry) of venous thromboembolic disease are eligible, but should receive prophylactic aspirin or low molecular weight heparin
* History of allergic reactions attributable to compounds of similar chemical or biologic composition to thalidomide, lenalidomide or any component of PCV7 or PCV13, including the diphtheria toxoid
* Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the subject is considered by his or her physician to have a 2 year survival expectation
* Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements
* Pregnant women are excluded from this study because lenalidomide is an immunomodulatory agent (IMID) with the potential for teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with lenalidomide, breastfeeding should be discontinued if the mother is treated with lenalidomide
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy will be eligible if they otherwise meet required hematologic parameters and are not receiving an antiviral agent with known or potential interaction with lenalidomide; because the primary aim of this study is to measure the immune response to pneumococcal vaccination, only patients with CD4 cell counts \>= 200 and viral load \< 50 will be eligible
* Patients who have been treated for autoimmune hemolytic anemia or autoimmune thrombocytopenia within the last 6 months or are direct antiglobulin test/Coombs test or indirect antiglobulin test positive at the time of screening
* Patients who have developed erythema nodosum characterized by a desquamating rash while taking thalidomide or similar drugs in the past are excluded
* Because of the potential for H2-blockers to modulate antibody response to pneumococcal vaccine, patients must discontinue treatment with H2-blockers (cimetidine, ranitidine, etc.) prior to beginning protocol therapy