Ibrutinib and Lenalidomide in Treating Patients With Myelodysplastic Syndrome

Inclusion Criteria: * Pathologically confirmed diagnosis of MDS by World Health Organization (WHO) criteria (including secondary and therapy-related disease) who have failed standard therapy, who are intolerant of prior therapy, or who refuse standard therapy; any prior therapy, including ibrutinib and/or lenalidomide (unless intolerant of one or both of these medications), is permitted * Hypomethylating agent failure is defined as disease progression or stable disease as best response to an adequate course of treatment (at least four cycles) with an injectable hypomethylating agent (azacitidine or decitabine) * International Prognostic Scoring System (IPSS)-revised (R) intermediate, high or very high risk disease * No specific hematologic parameters for study entry are required; transfusion-dependent patients are eligible and platelet counts should be maintained greater than 10,000/mm\^3 * Serum aspartate transaminase (AST) or alanine transaminase (ALT) less than or equal to 3.0 x upper limit of normal (ULN) * Estimated creatinine clearance greater than or equal to 60 ml/min (Cockcroft-Gault) * Bilirubin less than or equal to 1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin) * Prothrombin time (PT)/international normalized ratio (INR) less than or equal to 1.5 x ULN and partial thromboplastin time (PTT) (activated \[a\]PTT) less than or equal to 1.5 x ULN * Karnofsky performance status (KPS) performance status of 60% or greater * Ability to understand and willingness to sign an informed consent form * Ability to adhere to the study visit schedule and other protocol requirements * Female subjects who are of non-reproductive potential (i.e., post-menopausal by history - no menses for \>= 1 year; OR history of hysterectomy; OR history of bilateral tubal ligation; OR history of bilateral oophorectomy); or, female subjects of childbearing potential must have a negative serum pregnancy test upon study entry * Male and female subjects who agree to use highly effective methods of birth control (e.g., condoms, implants, injectables, combined oral contraceptives, some intrauterine devices \[IUDs\], sexual abstinence, or sterilized partner) during the period of therapy and for 30 days after the last dose of study drug * Females of reproductive potential must adhere to the scheduled pregnancy testing as required in the Revlimid Risk Evaluation and Mitigation Strategies (REMS) program * All study participants must be registered into the mandatory Revlimid REMS program, and be willing and able to comply with the requirements of the REMS program * Eligibility of patients receiving any medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of ibrutinib or ability to adhere to the Revlimid REMS program will be determined following review of their case by the principal investigator Exclusion Criteria: * Anticancer therapy including chemotherapy, immunotherapy, radiotherapy, hormonal or any investigational therapy within 14 days or 5 half-lives (whichever is shorter) prior to first dose of study drug; hydroxyurea is permitted up to the day before initiation of study treatment * Prior allogeneic (allo)-hematopoietic cell transplantation (HCT) less than three months from the time of enrollment * Acute graft versus host disease (GVHD) or active chronic GVHD greater than grade 1 * Concurrent systemic immunosuppressant therapy (e.g., cyclosporine A, tacrolimus, etc., or chronic administration \[\> 14 days\] of \> 60 mg/day of prednisone or equivalent) within 28 days of the first dose of study drug * History of allergy to or intolerance of ibrutinib or lenalidomide * Vaccinated with live, attenuated vaccines within 4 weeks of first dose of study drug * Recent culture-documented infection requiring systemic intravenous treatment that was completed =\< 7 days before the first dose of study drug or any uncontrolled active systemic infection; fever of unknown origin is not an exclusion criterion, as this may be disease-related * Unresolved toxicities from prior anti-cancer therapy, defined as having not resolved to Common Terminology Criteria for Adverse Event (CTCAE, version 4.03), grade 2 or less, or to the levels dictated in the inclusion/exclusion criteria with the exception of alopecia * Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia * History of stroke or intracranial hemorrhage within 3 months prior to enrollment * Active infection with human immunodeficiency virus (HIV), hepatitis C virus (HCV) or hepatitis B virus (HBV); subjects who are positive for hepatitis B core antibody, hepatitis B surface antigen, or hepatitis C antibody must have a negative polymerase chain reaction (PCR) result before enrollment; those who are PCR positive will be excluded; subjects with HIV must have a CD4 count at or above the institutional lower limit of normal and not taking prohibited CYP3A strong inhibitors * Major surgery within 4 weeks of first dose of study drug * Any life-threatening illness, medical condition, or organ system dysfunction, including but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, active autoimmune disorder, or psychiatric illness/social situations that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, adequately treated in situ carcinoma of the breast or cervix uteri, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin * Concomitant use of warfarin or other vitamin K antagonists * Subjects who received a strong cytochrome P 450 3A (CYP3A) inhibitor within 7 days prior to the first dose of ibrutinib or subjects who require continuous treatment with a strong CYP3A inhibitor * Currently active, clinically significant hepatic impairment Child-Pugh class B or C according to the Child Pugh classification * Lactating or pregnant patients or patients of reproductive potential not willing to use effective methods of contraception and adhere to the Revlimid REMS program * Participation in clinical trials with other investigational agents not included in this trial throughout the duration of this trial * Unwilling or unable to participate in all required study evaluations and procedures or unable to understand the purpose and risks of the study and to provide a signed and dated informed consent form (ICF) and authorization to use protected health information (in accordance with national and local subject privacy regulations)