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 che…