Lenalidomide and Alvocidib in Treating Patients With Relapsed or Refractory B-cell Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

Inclusion Criteria: * Histologically confirmed B-cell CLL/SLL according to World Health Organization (WHO) criteria, or B-cell prolymphocytic leukemia (B-PLL) arising from CLL with at least one of the following indications for treatment: * Progressive disease or marked splenomegaly and/or lymphadenopathy * Anemia (hemoglobin \< 11 mg/dL) or thrombocytopenia (platelets \< 100,000/mm\^3) * Unexplained weight loss exceeding 10% of body weight over the preceding 6 months * National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events version 4.0 (CTCAE v 4.0) grade 2 or 3 fatigue * Fevers \> 100.5 or night sweats for greater than 2 weeks without evidence of infection * Progressive lymphocytosis, with an increase exceeding 50% over a 2 month period or a doubling time of less than 6 months * Must have at least one prior therapy that includes either fludarabine (or equivalent nucleoside analogue) or an alternative regimen if a contra-indication to fludarabine exists (i.e., autoimmune hemolytic anemia); prior therapy with flavopiridol is not permitted; prior lenalidomide is permitted provided that it has been \> 6 months since the last lenalidomide dose * Eastern Cooperative Oncology Group (ECOG) performance status =\< (Karnofsky \>= 60%) * White blood cell count =\< 150,000/mm\^3 * Absolute neutrophil count \>= 1,000/mm\^3 * Platelets \>= 30,000/mm\^3 * Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN) * Aspartate aminotransferase (AS…