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 (AST) serum glutamic oxaloacetic transaminase (SGOT)/alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =\< 2.5 X institutional ULN
* Creatinine =\< 1.5 mg/dL OR creatinine clearance \>= 60 ml/min
* Recovery to =\< grade 1 from all toxicities associated with prior therapy
* Not pregnant or breast-feeding; woman of child bearing potential should have a negative pregnancy test (serum beta-human chorionic gonadotropin \[HCG\]) within 7-14 days of starting cycle 1 of treatment; woman of child bearing potential should have a negative pregnancy test (serum beta-HCG) within 10-14 days of starting cycle 2, the start of lenalidomide treatment (i.e. days 14-18 of cycle 1), and an additional test within 24 hours of starting cycle 2 treatment
* Patient must agree to use adequate contraception for 4 weeks prior to the start of lenalidomide and up to 28 days following the last dose of lenalidomide to avoid risk of pregnancy

  * Women of child-bearing potential will be required to use two methods of birth control; one "highly effective method" and one "additional effective method" as defined below:

    * Highly effective methods

      * Intrauterine device
      * Hormonal (oral contraceptive, implants)
      * Tubal ligation
      * Partner's vasectomy
      * Abstinence
    * Alternative effective methods

      * Latex condoms
      * Diaphragm
      * Cervical cap
  * Men must agree to use latex condoms
* 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 and again within 24 hours prior to starting cycle 1 of 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; all patients must be counseled by a trained counselor every 28 days about pregnancy precautions and risks of fetal exposure
* Patients must agree not to donate blood, semen, sperm/ova during the course of taking lenalidomide and for 28 days after stopping lenalidomide treatment
* Patients must have the ability to understand and the willingness to sign a written informed consent document
* Patients who are glucose-6-phosphate dehydrogenase (G6PD) deficient are not eligible for this study
* Only human immunodeficiency virus (HIV)-positive patients meeting all of the following criteria may be enrolled on this trial:

  * Cluster of differentiation (CD) 4 count \> 500/mm\^3
  * Not receiving highly active anti-retroviral therapy (HAART) or anti-HIV viral therapy
  * HIV viral load \< 10,000 HIV messenger ribonucleic acid (mRNA) copies/mm\^3
  * No history of acquired immune deficiency syndrome (AIDS)-defining illness

Exclusion Criteria:

* Patients may not be receiving any other investigational agents
* 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; breastfeeding should be discontinued if the mother is treated on this study