Ibrutinib in Treating Patients With Refractory or Relapsed Lymphoma After Donor Stem Cell Transplant

Inclusion Criteria: PRE-STEM CELL TRANSPLANT (SCT) * Patients undergoing their first T cell replete allo-HCT for chronic lymphocytic leukemia (CLL), Hodgkin Lymphoma (HL), or the following subtypes of Non-Hodgkin lymphoma: Mantle cell lymphoma (MCL) and follicular center cell lymphoma (FL) * Meeting institutional criteria for allo-HCT. Ejection fraction by echocardiogram or MUGA \>40%, pulmonary function test with adjusted DLCO ≥ 60% * Matched (8/8) or mismatched (7/8) related, unrelated HCT * Stem cell source: bone marrow, peripheral blood stem cell * Disease criteria: Cohort A Chronic lymphocytic leukemia * Disease burden: lymph node size \< 5 cm and/or extra-nodal involvement \< 5 cm AND * 17 p deletion (detected by any assay) (\> or equal to 20% of cells involved if assay is conventional cytogenetics or fluorescence in situ hybridization \[FISH\]) or NOTCH mutation at any time point during disease course; patient should have received at least 1 line of therapy; prior ibrutinib therapy is permitted OR * Relapsed/refractory chronic lymphocytic leukemia \> or equal to 2 lines of therapy; prior ibrutinib therapy is permitted Mantle cell lymphoma * Disease burden: lymph node size \< 5 cm and/or extra-nodal involvement \< 5 cm AND * Relapsed/refractory mantle cell lymphoma \> or equal to 1 line of therapy. Prior ibrutinib therapy is permitted. Prior autologous hematopoietic cell transplant is permitted. OR * Mantle cell lymphoma blastoid variant in first complete response (CR1) or high risk mantle cell lymphoma being considered for allo hematopoietic cell transplant in CR1 Cohort B Follicular lymphoma Disease burden: lymph node size \< 5 cm and/or extra-nodal involvement \< 5 cm AND Relapsed/refractory follicular lymphoma \> or equal to 2 lines of therapy. Prior ibrutinib therapy is permitted Hodgkin disease * Disease burden: lymph node size \< 5 cm and/or extra-nodal involvement \< 5 cm AND * Relapsed/refractory Hodgkin disease \> or equal to 2 lines of therapy. * Preparative regimen: both reduced intensity and ablative regimens are permitted. Each center will pre-specify the regimen they intend to use during the conduct of the study * Donor criteria: HLA ≥ 7/8 related or unrelated donors. * Women of childbearing potential and men who are sexually active must be practicing a highly effective method of birth control during and after the study consistent with local regulations regarding the use of birth control methods for subjects participating in clinical trials. Men must agree to not donate sperm during and after the study. For females, these restrictions apply for 1 month after the last dose of study drug. For males, these restrictions apply for 3 months after the last dose of study drug. * Women of childbearing potential must have a negative serum (beta-human chorionic gonadotropin \[beta-hCG\]) or urine pregnancy test at screening. Women who are pregnant or breastfeeding are ineligible for this study * Sign (or their legally-acceptable representatives must sign) an informed consent document indicating that they understand the purpose of and procedures required for the study, including biomarkers, and are willing to participate in the study * Prior to Administration of Ibrutinib (Day 60 to Day 90 post hematopoietic cell transplant) * Karnofsky performance status (KPS) \> or equal to 60% * Engraftment of neutrophils (absolute neutrophil count \[ANC\] \>= 1.0 X 10\^9/L) for 3 days without granulocyte colony-stimulating factor (g-csf) support * Platelets \> or equal to 100,000/mm\^3 or \> or equal to = 50,000/mm\^3 if bone marrow involvement independent of transfusion support in either situation * Glomerular filtration rate (GFR) \> or equal to 30 ml/min * Liver function tests (LFTs) (alanine aminotransferase \[ALT\] and aspartate aminotransferase \[AST\]) equal to or \< 3 X upper limit of normal (ULN) * Total bilirubin equal to or \< 1.5 mg/dL X ULN unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin * Predominant donor chimerisms of \> or equal to 51% as measured by CD3 and CD33 (or other myeloid marker) Exclusion Criteria: PRE-SCT * Progression of chronic lymphocytic leukemia or mantle cell lymphoma or follicular lymphoma or HD at time of transplant * Use of Coumadin (warfarin) or other vitamin-K antagonists for anticoagulation; non-Coumadin anticoagulation is permitted * Known central nervous system involvement * Active uncontrolled bacterial or invasive fungal infections * History of malignancy other than the underlying disease unless treated with a curative intent and/or no evidence of disease for at least 3 years (y) OR expected to be cured with SCT * Planned use of post-hematopoietic cell transplant cyclophosphamide for graft versus host disease prophylaxis * Anticipated planned donor lymphocyte infusion in the first 3 months post-SCT * T deplete hematopoietic cell transplant * Umbilical cord hematopoietic cell transplant * History of stroke or intracranial hemorrhage within 6 months of enrollment * Clinically significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any class 3 (moderate) or class 4 (severe) cardiac disease as defined by the New York Heart Association Functional Classification * Known HIV * Active Hepatitis B or C virus * Child-Pugh Class C PRIOR TO ADMINISTRATION OF IBRUTINIB (DAY 60-DAY 90 POST SCT) * In the critical care unit, or use of mechanical ventilation or use of renal replacement therapy at any time post hematopoietic cell transplant and prior to administration of ibrutinib * Active uncontrolled stage 3-4 acute gastrointestinal (GI) graft versus host disease prior to administration of ibrutinib * Active uncontrolled stage 4 acute liver graft versus host disease prior to administration of ibrutinib * Evidence of progressive disease as compared to pre-hematopoietic cell transplant (persistence of disease is permitted) * Anticipated planned donor lymphocyte infusion in the first 3 months post-SCT * Active uncontrolled bacterial or invasive fungal infections * Prednisone equivalent of \> 2m/kg for treatment of graft versus host disease prior to administration of ibrutinib * Use of second line systemic therapy for treatment of acute graft versus host disease prior to administration of ibrutinib * Any life-threatening illness, medical condition, or organ system dysfunction which, in the investigator's opinion, could compromise the subject's safety, interfere with the absorption or metabolism of ibrutinib capsules, or put the study outcomes at undue risk. Including the presence of chronic/active HBV and HBC infections and Child-Pugh Class C.ibrutinib. * Major surgery or a wound that has not fully healed within 4 weeks of starting. * Requires anticoagulation with warfarin or equivalent vitamin K antagonists (e.g., phenprocoumon) * Requires chronic treatment with strong cytochrome P450, family 3, subfamily A (CYP3A) inhibitors * Vaccinated with live, attenuated vaccines within 4 weeks of starting ibrutinib