Lenalidomide and Combination Chemotherapy in Treating Patients With Relapsed or Refractory Acute Myeloid Leukemia

Inclusion Criteria: * Patients eligible include those with diagnosis of AML other than acute promyelocytic leukemia by World Health Organization (WHO) criteria with relapsed disease after induction therapy or refractory to induction chemotherapy, as determined by morphology on bone marrow biopsy; also eligible are patients unwilling to receive standard induction chemotherapy * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Serum creatinine =\< 1.5 mg/dL; if serum creatinine \> 1.5 mg/dL, then the estimated glomerular filtrate rate (GFR) must be \> 60ml/min/1.73m\^2 as calculated by the Modification of Diet in Renal Disease equation * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) unless elevation is considered to be secondary to Gilbert's syndrome, hemolysis, or hepatic infiltration by AML * Aspartate transaminase (AST)/alanine transaminase (ALT) =\< 2.5 x ULN * Alkaline phosphatase =\< 2.5 x ULN * All study participants must be registered into the mandatory Revlimid assistance (RevAssist) program, and be willing and able to comply with the requirements of RevAssist * Females of childbearing potential (FCBP) must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10 - 14 days and again within 24 hours prior to prescribing lenalidomide for cycle 1 (prescriptions must be filled within 7 days as required by RevAssist) and 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 she starts taking 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 Exclusion Criteria: * Patient must not undergo concomitant radiotherapy, chemotherapy or immunotherapy; patient must not be in concurrent study with other investigational agents * Patients who have received prior lenalidomide therapy are not eligible for this study; further there should be at least a 14-day window from the patient's last prior therapy before initiation of treatment on clinical trial * Have other severe concurrent disease or serious organ dysfunction involving the heart, kidney, liver or other organ system that may place the patient at undue risk to undergo treatment * Have significant, uncontrolled active infection * Pregnant or nursing patients will be excluded from the study * Known human immunodeficiency virus (HIV) infection