Lirilumab and Azacitidine in Treating Patients With Refractory or Relapsed Acute Myeloid Leukemia

Inclusion Criteria: * Patients with AML or biphenotypic or bilineage leukemia who have failed at least one prior therapy; patients with AML should have failed prior therapy or have relapsed after prior therapy * Patients should not be eligible or able to receive approved therapy of confirmed clinical benefit in this patient population * Patients with myelodysplastic syndrome (MDS) or chronic myelomonocytic leukemia (CMML) who received therapy for the MDS or CMML and progress to AML are eligible at the time of diagnosis of AML regardless any prior therapy for AML; the World Health Organization (WHO) classification will be used for AML * Prior therapy with hydroxyurea, chemotherapy, biological or targeted therapy (e.g. FLT3 inhibitors, other kinase inhibitors), or hematopoietic growth factors is allowed * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Total bilirubin =\< 2 times upper limit of normal (x ULN) (=\< 3 x ULN if considered to be due to leukemic involvement or Gilbert's syndrome) * Aspartate aminotransferase or alanine aminotransferase =\< 2.5 x ULN (=\< 5.0 x ULN if considered to be due to leukemic involvement) * Serum creatinine =\< 2 x ULN or glomerular filtration rate (GFR) \>= 50 * Patients must provide written informed consent * In the absence of rapidly progressing disease, the interval from prior treatment to time of initiation of 5-azacytidine and lirilumab will be at least 2 weeks OR at least 5 half-lives for cytotoxic/noncytotoxic agents; use of one dose of cytarabine (up to 2 g/m\^2) is allowed prior to the start of study therapy or hydroxyurea for patients with rapidly proliferative disease is allowed before the start of study therapy and while the patient is on active study treatment, as needed, for clinical benefit and after discussion with the principal investigator (PI); concurrent therapy for central nervous system (CNS) prophylaxis or continuation of therapy for controlled CNS disease is permitted * Females must be surgically or biologically sterile or postmenopausal (amenorrheic for at least 12 months) or if of childbearing potential, must have a negative serum or urine pregnancy test within 72 hours before the start of the treatment * Women of childbearing potential must agree to use an adequate method of contraception during the study and until 30 days after the last treatment; males must be surgically or biologically sterile or agree to use an adequate method of contraception during the study until 30 days after the last treatment; women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential Exclusion Criteria: * Patients with known allergy or hypersensitivity to lirilumab, 5-azacytidine, or any of their components; patients who have previously been treated with lirilumab in combination with 5-azacytidine will be excluded * Patients with a known history of severe interstitial lung disease or severe pneumonitis or active pneumonitis that is uncontrolled in the opinion of the treating physician * Patients with a known history of any of the following autoimmune diseases are excluded: (a) patients with a history of inflammatory bowel disease (including Crohn's disease and ulcerative colitis) (b) patients with a history of rheumatoid arthritis, systemic progressive sclerosis \[scleroderma\], systemic lupus erythematosus, autoimmune vasculitis \[e.g., Wegener's granulomatosis\]) * Patients with organ allografts (such as renal transplant) are excluded * Patients with allogeneic stem cell transplantation within the last 6 months or patients with active graft-versus-host disease (GVHD) will be excluded * Ongoing immunosuppressive therapy, including cyclosporine and tacrolimus; patients who are on high dose steroid; Note: Subjects may be using systemic corticosteroids (daily doses =\< 10 mg of prednisone or equivalent) or topical or inhaled corticosteroids * Patients with symptomatic CNS leukemia or patients with poorly controlled CNS leukemia * Active and uncontrolled disease/(active uncontrolled infection, uncontrolled hypertension despite adequate medical therapy, active and uncontrolled congestive heart failure New York Heart Association \[NYHA\] class III/IV, clinically significant and uncontrolled arrhythmia) as judged by the treating physician * Patients with active and uncontrolled human immunodeficiency virus (HIV) infection will be excluded; however, patients with well controlled HIV infection will be considered * Patients known to be positive for hepatitis B by surface antigen expression; known to have active hepatitis C infection (positive by polymerase chain reaction or on antiviral therapy for hepatitis C within the last 6 months) * Any other medical, psychological, or social condition that may interfere with study participation or compliance, or compromise patient safety in the opinion of the investigator * Patients unwilling or unable to comply with the protocol * Pregnant or breastfeeding * Acute promyelocytic leukemia (APL)