Fludarabine and Rituximab With or Without Lenalidomide or Cyclophosphamide in Treating Patients With Symptomatic Chronic Lymphocytic Leukemia

Inclusion Criteria: * Specific diagnosis of B-cell CLL: * An absolute lymphocytosis of \> 5,000/uL * Morphologically, the lymphocytes must appear mature with \< 55% prolymphocytes * Bone marrow examination must include at least a unilateral aspirate and biopsy; the aspirate smear must show \> 30% of all nucleated cells to be lymphoid or the bone marrow core biopsy must show lymphoid infiltrates compatible with marrow involvement by CLL; overall cellularity must be normocellular or hypercellular * Local institution lymphocyte phenotype must reveal a predominant B-cell monoclonal population sharing a B-cell marker (cluster of differentiation \[CD\]19, CD20, CD23) with the CD5 antigen, in the absence of other pan-T-cell markers; additionally, the B-cells must be monoclonal with regard to expression of either kappa or lambda and have surface immunoglobulin expression of low density; patients with bright surface immunoglobulin levels must have CD23 co-expression * Patients must have symptomatic and active intermediate or high-risk categories of the modified three-stage Rai staging system: * Not eligible: low risk, Rai stage 0, lymphocytes (L) in blood (\> 5000/uL) and marrow (\> 30%) only * Intermediate risk, Rai stage I, L + enlarged lymph nodes (LN) * Intermediate risk, Rai stage II, L + spleen and/or liver (LN + or -) * High risk, Rai stage III, L + anemia (hemoglobin \< 11 gm/dL) * High risk, Rai stage IV, L + thrombocytopenia (platelets \< 100,000/uL) * Patients in the intermediate-risk group must have evidence of active disease as demonstrated by at least one of the following criteria: * Massive or progressive splenomegaly, hepatomegaly and/or lymphadenopathy * Presence of weight loss \> 10% over the preceding 6 month period * Grade 2 or 3 fatigue * Fevers \> 100.5 degrees Fahrenheit (°F) or night sweats for greater than 2 weeks without evidence of infection * Progressive lymphocytosis with an increase of \> 50% over a 2 month period or an anticipated doubling time of less than 6 months * No prior therapy for CLL, including no corticosteroids for autoimmune complications that have developed since the initial diagnosis of CLL * No medical condition requiring chronic use of oral corticosteroids * Performance status 0 - 2 * Patients with human immunodeficiency virus (HIV) infection may be eligible provided they meet the following criteria: no evidence of infection with hepatitis B or C; CD4+ cell count \> 350/mm\^3; no evidence of resistant strains of HIV; if not on anti-HIV therapy, an HIV viral load \< 10,000 copies HIV ribonucleic acid (RNA)/mL; if on HIV therapy, HIV viral load \< 50 copies HIV RNA/mL; and no history of acquired immune deficiency syndrome (AIDS)-defining condition; patients receiving concurrent zidovudine or stavudine may not be enrolled * Non-pregnant and non-nursing * In females of child-bearing potential randomized to Arm B or assigned to Arm D, a negative urine or serum pregnancy test with a sensitivity of at least 25 mIU/mL will be required: 1) 10-14 days prior to beginning lenalidomide consolidation therapy; and 2) within 24 hours prior to the first dose of lenalidomide consolidation therapy; in addition, females of childbearing potential in Arm B and Arm D with regular menses must have a pregnancy test performed weekly during the first 28 days of treatment, and then every 28 days while taking lenalidomide (including breaks in lenalidomide), at discontinuation of lenalidomide, and then 28 days following discontinuation of lenalidomide; if menses are irregular, a pregnancy test must be performed weekly during the first 28 days of treatment, and then every 14 days while taking lenalidomide, at discontinuation of lenalidomide, and at 14 and 28 days after discontinuation of lenalidomide; additionally, females of childbearing potential must either commit to continued abstinence from heterosexual intercourse or begin TWO reliable methods of birth control - one highly effective method (intrauterine device \[IUD\], hormonal \[birth control pills, injections, or implants\], tubal ligation, or partner's vasectomy), and one additional effective method (latex condom, diaphragm, or cervical cap) - AT THE SAME TIME, at least 4 weeks before she begins lenalidomide therapy, while participating in the study, and for at least 4 weeks after completing lenalidomide therapy; "females of childbearing potential" is defined as a sexually mature woman who has not undergone a hysterectomy or bilateral oophorectomy, or who has had menses at any time in the preceding 24 consecutive months (not been naturally postmenopausal for at least 24 consecutive months) * Male patients randomized to Arm B or reassigned to Arm D must agree not to father a child and to use a latex condom during any sexual contact with females of childbearing potential while taking lenalidomide and for at least 4 weeks following completion of lenalidomide therapy, even if the patient have undergone a successful vasectomy * All patients randomized to Arm B or reassigned to Arm D must be counseled by a trained counselor every 28 days during consolidation therapy about pregnancy precautions and risks of fetal exposure * Creatinine =\< 1.5 x upper limit of normal