Lenalidomide With or Without Epoetin Alfa in Treating Patients With Myelodysplastic Syndrome and Anemia

Inclusion Criteria: * Age \>= 18 years * NOTE: Results of the bone marrow biopsy and aspirate as well as cytogenetics are mandatory to register subjects onto study, which are indispensable to determine International Prognostic Scoring System (IPSS) category needed for eligibility; please note that it is not necessary to wait for the week 16, week 32, or week bone marrow and cytogenetic results prior to starting the next cycle unless deemed necessary by the treating physician; one example of this exception can include if the subject shows signs of progression, such as increased peripheral blood blast percentage; at that juncture, the treating physician may prefer to await the results prior to starting a new cycle; if a cycle is started, and based on the bone marrow results it is felt by the treating physician that the subject should not continue on treatment, please be sure to note this information on the case report forms at end of treatment * Patient must have documented diagnosis of MDS lasting at least three months (MDS duration \>= 3 months) according to World Health Organization (WHO) criteria or non-proliferative chronic myelomonocytic leukemia (CMML) (white blood cell \[WBC\] \< 12,000/mcL) * Patient must have International Prognostic Scoring System (IPSS) categories of low- or intermediate-1-risk disease; patients must have IPSS score determined by cytogenetic analysis prior to randomization; patients must have cytogenetic analysis done (to calculate IPSS); if the current bone marrow biopsy is a dry tap, patients with cytogenetic failure and \< 10% marrow blasts will be eligible; subjects with cytogenetic failure must have previous cytogenetic results (fluorescence in situ hybridization \[FISH\] is not a substitute) within the last 6 months post last type of MDS treatment (in this case, not referring to growth factors as type of MDS treatment) * Must have symptomatic anemia untransfused with hemoglobin \< 9.5 g/dL =\< 8 weeks prior to randomization or with red blood cells (RBC) transfusion dependence (i.e., \>= 2 units/month) confirmed for =\< 8 weeks before randomization * NOTE: For non-transfusion dependent patients (i.e., receiving \< 2 units/4 weeks x 8 weeks pre-study) who receive periodic transfusions, the mean 8 week pre-transfusion hemoglobin should be used to determine protocol eligibility and response reference * For non-transfusion dependent patients, a minimum of 2 pre-transfusion or un-transfused hemoglobin values are required * Applies only for patients without the deletion 5q 31.1; patients must have failed treatment with an erythropoietic growth factor, or have a low probability of response to rhu-erythropoietin; patients with low probability of response to rhu-erythropoietin or prior erythropoietin failures are defined as follows: * Prior erythropoietin failure-requires a minimum trial of \>= 40,000 units epoetin alfa/week x 8 weeks or equivalent dose of darbepoetin alfa for 8 weeks with failure to achieve transfusion independence in dependent patients or a failure to achieve a \>= 2 g rise in hemoglobin sustained for \>= 4 weeks in non-transfusion dependent patients * Low erythropoietin response profile-rhu-erythropoietin and epoetin alfa-naïve patients receiving \>= 2U packed (p)RBC/month for a minimum of 8 weeks, and serum erythropoietin \> 500 mU/mL in the 8 weeks prior to randomization for a hemoglobin \< 9.5 g/dL * Patients must be off all non-transfusion therapy for MDS for 28 days prior to initiation of study treatment, including all types of growth factors; patients may receive hydrocortisone prophylactically to prevent transfusion reactions * Patients must have a serum erythropoietin level documented before randomization and =\< 56 days before day 1 of study treatment; NOTE: hemoglobin must be \< 9.5 g/dL at time that serum erythropoietin is drawn * Effective contraception must be used by patients participating in lenalidomide therapy, and all patients must agree to counseling by a trained counselor every 28 days about pregnancy precautions and risks of fetal exposure; females of childbearing potential (FCBP) 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, during lenalidomide therapy, during dose interruptions, and for at least 28 days following discontinuation of lenalidomide therapy; females of childbearing potential should be referred to a qualified provider of contraceptive methods, if needed; males receiving lenalidomide must agree to use a latex condom during any sexual contact with females of childbearing potential even if they have undergone a successful vasectomy * Platelet count \>= 50,000/mcL (50 x 10\^9/L) without platelet transfusion (within 56 days prior to randomization) * Absolute neutrophil count (ANC) \>= 500 cells/mcL (0.5 x 10\^9/L); hence ANC must be \>= 500/mcL without myeloid growth factor support (within 56 days prior to randomization) * Serum creatinine =\< 1.5 times upper limit of normal (ULN) (within 56 days prior to randomization) * Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) or serum glutamate pyruvate transaminase (SGPT)/alanine aminotransferase (ALT) =\< 2.0 x ULN (within 56 days prior to randomization) * Serum total bilirubin \< 3.0 mg/dL (within 56 days prior to randomization) * Inclusion criteria for crossover registration from Arm A (lenalidomide alone) to Arm B (lenalidomide and epoetin alfa): * Patients must have completed 16 weeks of monotherapy with lenalidomide * Patients must show failure to achieve MER (major erythroid response) or have achieved MER but relapsed on Arm A Exclusion Criteria: * Patients must not have documented iron deficiency; all patients must have documented marrow iron stores; if marrow iron stain is not available, the transferrin saturation must be \> 20% or a serum ferritin \> 100 ng/mL * Women must not be pregnant or breastfeeding; females of childbearing potential 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; a female of childbearing potential (FCBP) is any woman, regardless of whether they have undergone tubal ligation, who meets the following criteria: 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; FCBP must also agree to ongoing pregnancy testing) * Patients must not have prior therapy with lenalidomide * Patients must not have a diagnosis of uncontrolled seizure or uncontrolled hypertension * Patients must not have proliferative (WBC \>= 12,000/mcL) chronic myelomonocytic leukemia (CMML); WBC must be \< 12,000/mcL * Patients must not have MDS secondary to treatment with radiotherapy, chemotherapy, and/or immunotherapy for malignant or autoimmune diseases * Prior thalidomide therapy is allowed, however, patients must not have prior \>= grade-3 allergic reactions to thalidomide * Patients must not have prior history of desquamating rash from thalidomide at time of study entry * Patients must not have clinically significant anemia resulting from iron, B12 or folate deficiencies, autoimmune or hereditary hemolysis, or gastrointestinal bleeding * Patients must not have used cytotoxic chemotherapeutic agents or experimental agents (agents that are not commercially available) for the treatment of MDS within 8 weeks of randomization * Patients must not have prior history of malignancy other than MDS (except basal cell or squamous skin cell carcinoma or carcinoma in situ of the cervix or breast) unless the subject has been confirmed free of disease for \>= 3 years * Patients must not have any serious medical condition or any other unstable medical co-morbidity, or psychiatric illness that will prevent the subject from signing the informed consent form or will place the subject at unacceptable risk if he/she participates in the study * Patients must not have a history of thrombo-embolic events within 3 years prior to study randomization * Patients must not have known human immunodeficiency virus (HIV)-1 seropositivity because HIV can be an alternate cause of anemia. * Patients must not have a known allergic reaction to epoetin alfa (Procrit) or human serum albumin * Exclusion criteria for crossover registration from Arm A (lenalidomide alone) to Arm B (lenalidomide and epoetin alfa): * Patients must not have a limiting unresolved grade 3 or greater toxicity from lenalidomide monotherapy or drug intolerance preventing continuation of lenalidomide treatment