Patient does not have any documented history of central nervous system (CNS) involvement by mantle cell lymphoma; this includes no evidence of parenchymal brain, spinal cord, or cerebrospinal fluid involvement; radiculopathy symptoms from nerve root compression by lymphoma do not constitute CNS involvement Patients with a known central nervous system (CNS) involvement of lymphoma are not eligible (CNS staging not required) Participants with evidence for central nervous system (CNS) lymphoma on neurological exam and/or with radiographic evidence (if radiographic studies are done) of CNS lymphoma (inclusive of parenchymal, vitreal, or leptomeningeal involvement) Known active central nervous system (CNS) involvement by lymphoma, including parenchymal and/or lymphomatous meningitis Patients with known central nervous system (CNS) involvement of lymphoma are not eligible Active, uncontrolled central nervous system (CNS) involvement by lymphoma CNS lymphoma. Patients must not have known central nervous system (CNS) involvement of lymphoma Central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells Patients with known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement Known active central nervous system (CNS) involvement by lymphoma should be excluded from this clinical trial Known central nervous system (CNS) involvement by lymphoma Active central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells that requires therapy Central nervous system (CNS) involvement by lymphoma/leukemia Patients with active known central nervous system (CNS) involvement of CLL or lymphoma; (patients with history of CNS CLL or lymphoma now in remission are eligible for the trial) Known central nervous system (CNS) involvement by lymphoma; patients at high risk for secondary CNS involvement but without neurologic symptoms suspected to be due to lymphoma are allowed to be enrolled and receive intrathecal chemotherapy including but not limited to methotrexate, cytarabine and glucocorticoids; patients who are enrolled and subsequently identified to have pathologic confirmation of CNS involvement by lymphoma may be continued on study at the discretion of the principal investigator Symptomatic or untreated Central nervous system (CNS) disease, Subjects with a history of CNS disease (leukemia, lymphoma or myeloma) are permitted to enrol if they have previously received appropriate therapy and CNS remission has been documented. Subject with primary CNS lymphoma (defined as isolated CNS lymphoma without systemic involvement) are excluded from study. Active central nervous system (CNS) involvement by lymphoma, including untreated symptomatic epidural disease Patients with active central nervous system (CNS) involvement with lymphoma are not eligible Known central nervous system (CNS) involvement by lymphoma Has known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement; subjects with prior CNS involvement by lymphoma must have remission of the CNS component of the lymphoma; these subjects must have a baseline magnetic resonance imaging (MRI) during screening without evidence of new or enlarging brain lesions and must not have any new or progressive neurologic symptoms Patients with a history of central nervous system (CNS) involvement by lymphoma or with relapsed primary CNS lymphoma will be eligible for cyclophosphamide (Cy)/TBI arm; patients with active CNS disease are eligible if they have completed a standard treatment for CNS lymphoma and have no evidence of progressive CNS disease at the time of enrollment Patients with active central nervous system (CNS) involvement with lymphoma are not eligible Central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) or meningeal involvement, or cord compression by the lymphoma; history of CNS lymphoma Central nervous system (CNS) involvement by lymphoma (clinically or cytologically confirmed) Central nervous system (CNS) lymphoma: CNS involvement by lymphoma, including parenchymal brain or spinal cord lymphoma or known presence of leptomeningeal disease prior to registration Primary CNS lymphoma Patients with active central nervous system (CNS) lymphoma or active cerebrospinal fluid (CSF) involvement with malignant cells requiring CNS-specific therapy with IV or intrathecal (IT) methotrexate (MTX); Note: Patients with any prior CNS lymphoma (parenchymalor leptomeningeal) MUST be in complete remission (CR) in those compartments without any maintenance therapy required Known central nervous system (CNS) involvement with lymphoma. Active central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells that requires therapy Patients must have no known central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) involvement by lymphoma including parenchymal brain or spinal cord lymphoma or known presence of leptomeningeal disease prior to registration Patients with a history of central nervous system (CNS) involvement by lymphoma or with relapsed primary CNS lymphoma will be eligible; patients with active CNS disease are eligible if they have completed a standard treatment for CNS lymphoma and have no evidence of progressive CNS disease at the time of enrollment Patients must not have clinical evidence of central nervous system (CNS) involvement by lymphoma \r\n* Any laboratory or radiographic tests performed to assess CNS involvement must be negative and must be performed within days prior to registration Central nervous system (CNS) involvement by lymphoma/leukemia CNS lymphoma involvement Subject who has central nervous system (CNS) or meningeal involvement by lymphoma. Current or history of CNS lymphoma Active CNS lymphoma. Patients with active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma Symptomatic central nervous system (CNS) lymphoma involvement Primary CNS lymphoma or evidence of CNS involvement by lymphoma Central nervous system (CNS) involvement by lymphoma Phase II: Patients with untreated, relapsed or refractory T-cell lymphoma, including patients with central nervous system (CNS) involvement or lymphomatous meningitis are allowed on study Primary central nervous system (CNS) lymphoma or known or suspected CNS involvement by non-primary CNS NHL Known central nervous system (CNS) involvement of lymphoma Central nervous system (CNS) involvement of the patient's lymphoma Patients with active central nervous system (CNS) involvement with lymphoma should be excluded from this clinical trial No active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma; a lumbar puncture demonstrating mantle cell lymphoma at the time of registration to this study is not an exclusion for study enrollment Known central nervous system (CNS) involvement by lymphoma. Known central nervous system (CNS) lymphoma involvement Known CNS involvement of indolent lymphoma Current central nervous system (CNS) involvement by lymphoma CNS or leptomeningeal involvement of lymphoma Known active cerebral/meningeal involvement with lymphoma; asymptomatic patients with previously treated and resolved central nervous system (CNS) lymphoma involvement are permitted Active central nervous system (CNS) lymphoma/leukemia - Patients with prior CNS involvement are eligible provided that it has been treated and is in remission Clinical evidence of CNS involvement by lymphoma Known primary CNS lymphoma Central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells Known Central Nervous System (CNS) involvement by lymphoma. Presence of central nervous system (CNS) involvement with Hodgkin lymphoma Central nervous system (CNS) lymphomatous involvement or leptomeningeal lymphoma Active central nervous system (CNS) lymphoma or cerebrospinal fluid involvement with malignant lymphoma cells that requires therapy Known presence of central nervous system (CNS) involvement by lymphoma Patients with central nervous system (CNS) lymphoma are not eligible for the trial unless the disease had been treated and the subject remains without symptoms with no active CNS lymphoma. Participants with known central nervous system (CNS) involvement of lymphoma Known central nervous system (CNS) involvement of lymphoma (CNS staging not required)