I. To increase the incidence of successful outcome (defined as lack of requirement of second line therapy for acute graft-versus-host disease, lack of National Institutes of Health [NIH] severe chronic graft-versus-host disease, lack of progression or relapse of chronic lymphocytic leukemia/mantle cell lymphoma [MCL], lack of death from disease or non-relapse causes) to at least 60% at 1 year post hematopoietic cell transplant. (Cohort A) II. To study the safety and tolerability of ibrutinib post hematopoietic cell transplant in patients with non-Hodgkin lymphoma (NHL) and Hodgkin lymphoma. (Cohort A and B combined) III. To study the incidence of grade 3-4 acute graft-versus-host disease in the first 6 months post hematopoietic cell transplant in patients with non-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) IV. To study the incidence of second line therapy (systemic only) for acute graft-versus-host disease in the first 6 months post hematopoietic cell transplant in patients with non-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) V. To study the incidence of recurrent acute graft-versus-host disease in the first 6 months post hematopoietic cell transplant in patients with non-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) VI. To study the incidence and severity of chronic graft-versus-host disease in the first 12 months post hematopoietic cell transplant in patients with not-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) VII. To study the incidence of lung involvement with graft-versus-host disease in the first 12 months post hematopoietic cell transplant in patients with non-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) VIII. To study the incidence of sclerotic skin chronic graft-versus-host disease in the first 12 months post hematopoietic cell transplant in patients with non-Hodgkin lymphoma and Hodgkin lymphoma. (Cohort A and B combined) IX. To study the incidence of infectious deaths not related to graft-versus-host disease in patients with non-Hodgkin and Hodgkin lymphoma. (Cohort A and B combined)