Ibrutinib and Rituximab in Treating Patients With Relapsed or Refractory Mantle Cell Lymphoma or Older Patients With Newly Diagnosed Mantle Cell Lymphoma

Inclusion Criteria: * Relapsed/refractory MCL: Confirmed diagnosis of mantle cell lymphoma with cluster of differentiation (CD)20 and cyclin D1 through cyclin D3 positivity in tissue biopsy * Relapsed/refractory MCL: Patient has relapsed and or refractory MCL and must have received at least one prior treatment regimen for their disease; patient with leukemia phase (peripheral blood involvement), leptomeningeal disease, cerebral spinal fluid (CSF) MCL, central nervous system (CNS) MCL, non-measurable disease, gastrointestinal (GI) MCL, or bone marrow (BM) MCL are also eligible * Relapsed/refractory MCL: Understand and voluntarily sign an Institutional Review Board (IRB)-approved informed consent form * Relapsed/refractory MCL: Patients with bone marrow or gastrointestinal (GI) only involvement are acceptable * Relapsed/refractory MCL: Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less * Relapsed/refractory MCL: Absolute neutrophil count (ANC) \>= 500/mm\^3; (patients who have bone marrow infiltration by MCL are eligible if their ANC is \>= 500/mm\^3 \[growth factor allowed\]; these patients should be discussed with either the principal investigator \[PI\] or Co-PI of the study for final approval) * Relapsed/refractory MCL: Platelet count \>= 30,000/mm\^3 (transfusion to reach platelet count allowed); (patients who have bone marrow infiltration by MCL are eligible if their platelet level is equal to or \> than 15,000/mm\^3; these patients should be discu…