Patients must not have clinical evidence of central nervous system involvement by lymphoma; if performed, any laboratory or radiographic tests performed to assess central nervous system (CNS) involvement must be negative Symptomatic or progressing or steroid requiring Central Nervous System (CNS) involvement disease at least four weeks prior to randomization Known central nervous system (CNS) involvement Patients with a known central nervous system (CNS) involvement of lymphoma are not eligible (CNS staging not required) Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy Current or past history of central nervous system (CNS) disease, or CNS involvement by MM Central nervous system (CNS) involvement Patients with known central nervous system (CNS) involvement of lymphoma are not eligible Evidence of leukemic meningitis or other central nervous system (CNS) involvement by leukemia Patients must not have known central nervous system (CNS) involvement of lymphoma Has clinical signs of central nervous system (CNS) involvement of MM. Known central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) involvement by lymphoma/leukemia Known central nervous system (CNS) involvement by malignancy Patients with central nervous system (CNS) involvement refractory to intrathecal chemotherapy and/or standard cranial-spinal radiation Known central nervous system (CNS) involvement with CLL or T-LGL Prior central nervous system (CNS) involvement by tumor cells; Known central nervous system (CNS) involvement Patients with history of central nervous system (CNS) involvement Known central nervous system (CNS) involvement The toxicity profile of nivolumab in patients with disease involvement of the central nervous system (CNS) is unknown Known central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) involvement, including lymphomatous meningitis Prior central nervous system (CNS) involvement by tumor cells Participant has known Central Nervous System (CNS) involvement with AML. History of plasma cell leukemia or multiple myeloma (MM) central nervous system (CNS) involvement Known central nervous system (CNS) involvement Central nervous system (CNS) involvement Uncontrolled central nervous system (CNS) involvement by tumor cells within the past 2 months Central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) involvement Central nervous system (CNS) involvement by lymphoma (clinically or cytologically confirmed) Patients with known central nervous system (CNS) involvement Known brain metastases or central nervous system (CNS) involvement Known central nervous system (CNS) tumor involvement History of plasma cell leukemia or MM central nervous system (CNS) involvement Central nervous system (CNS) involvement Patients with history of extramedullary AML, except for central nervous system (CNS) involvement that is currently controlled, will not be eligible for enrollment Central nervous system (CNS) involvement within 3 months Patient must have no current or prior history of central nervous system (CNS) involvement Patients with known central nervous system (CNS) involvement Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy Patients with known central nervous system (CNS) involvement by leukemia History of plasma cell leukemia or central nervous system (CNS) involvement Known central nervous system (CNS) involvement with lymphoma. Patient has distant metastatic disease, including central nervous system (CNS) tumor involvement Patients with central nervous system (CNS) involvement unless they meet ALL of the following criteria: Symptomatic central nervous system (CNS) involvement by AML Untreated central nervous system (CNS) involvement Uncontrolled central nervous system (CNS) disease involvement AML central nervous system (CNS) involvement Patients with central nervous system (CNS) involvement refractory to intrathecal chemotherapy Patients must have no known central nervous system (CNS) involvement by lymphoma Central nervous system (CNS) involvement by lymphoma/leukemia Patients who have symptomatic central nervous system (CNS) involvement are not eligible Central nervous system (CNS) involvement. Patients with documented central nervous system (CNS) involvement Patient must have no known central nervous system (CNS) involvement Known central nervous system (CNS) involvement by malignancy Known central nervous system (CNS) involvement Symptomatic central nervous system (CNS) lymphoma involvement Subjects with known or suspected central nervous system (CNS) involvement are not eligible Patients with known central nervous system (CNS) involvement are excluded from this clinical trial Central nervous system (CNS) involvement by CLL. Research participants with known brain metastases (central nervous system [CNS] involvement either parenchymal or leptomeningeal involvement) Has evidence of uncontrolled central nervous system (CNS) involvement (previous radiation and off steroids is acceptable) 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 History of central nervous system (CNS) involvement by myeloma Known central nervous system (CNS) involvement of lymphoma Known central nervous system (CNS) involvement Central nervous system (CNS) involvement of the patient's lymphoma Patients with central nervous system (CNS) involvement refractory to intrathecal chemotherapy and/or standard cranial-spinal radiation Patients with central nervous system (CNS) involvement Known central nervous system (CNS) involvement Known central nervous system (CNS) involvement by lymphoma. Uncontrolled central nervous system (CNS) involvement with disease Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy Known central nervous system (CNS) lymphoma involvement Evidence of AML central nervous system (CNS) involvement Central nervous system (CNS) involvement. Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy and/or standard cranial-spinal radiotherapy Central nervous system (CNS) involvement with disease refractory to intrathecal chemotherapy Patient has central nervous system metastatic involvement. Patients with previously treated CNS metastases are also excluded. Known central nervous system lymphoma or ALL with central nervous system (CNS) involvement Central nervous system (CNS) involvement of DLBCL Current central nervous system (CNS) involvement by lymphoma Known central nervous system (CNS) involvement Symptomatic central nervous system (CNS) involvement Symptomatic central nervous system (CNS) involvement Symptomatic, steroid-requiring or progressive central nervous system (CNS) involvement Clinically uncontrolled central nervous system (CNS) involvement Patients with central nervous system (CNS) metastatic involvement. Clinically uncontrolled central nervous system (CNS) involvement Patients must not have clinical evidence of central nervous system involvement by lymphoma, since proposed treatment would not be able to address it adequately; any laboratory (e.g., lactate dehydrogenase [LDH]) or radiographic tests performed to access central nervous system (CNS) involvement must be negative and must be performed within 42 days prior to registration Known central nervous system (CNS) involvement Known Central Nervous System (CNS) involvement by lymphoma. Presence of central nervous system (CNS) involvement with Hodgkin lymphoma Uncontrolled central nervous system (CNS) involvement by tumor cells Central nervous system (CNS) lymphomatous involvement or leptomeningeal lymphoma History of central nervous system (CNS) involvement Known presence of central nervous system (CNS) involvement by lymphoma Known central nervous system (CNS) involvement Patients with known central nervous system (CNS) involvement Participants with known central nervous system (CNS) involvement of lymphoma Known central nervous system (CNS) involvement Known central nervous system (CNS) involvement by AML Patients must not have known central nervous system (CNS) involvement Patients with known central nervous system (CNS) involvement Known central nervous system (CNS) involvement of lymphoma (CNS staging not required) Clinical signs of central nervous system (CNS) involvement of MM.