Alisertib in Combination With Vorinostat in Treating Patients With Relapsed or Recurrent Hodgkin Lymphoma, B-Cell Non-Hodgkin Lymphoma, or Peripheral T-Cell Lymphoma

Inclusion Criteria: * Patients must have a histologically or cytologically confirmed lymphoid malignancy (like Hodgkin lymphoma or one of the mature B- or T-cell non-Hodgkin lymphomas as classified by World Health Organization \[WHO\]) for which standard curative or palliative measures do not exist or are no longer effective * Patients must have measurable disease in two dimensions and \>= 2 cm is acceptable (or 1.5 cm if 0.5 slices are used, as in spiral computed tomography \[CT\] scans); lesions that are considered intrinsically non-measurable include the following: * Bone lesions * Leptomeningeal disease * Ascites * Pleural/pericardial effusion * Inflammatory breast disease * Lymphangitis cutis/pulmonis * Abdominal masses that are not confirmed and followed by imaging techniques * Cystic lesions * Lesions that are situated in a previously irradiated area * Patients must have had at least 1 prior systemic chemotherapy (not just steroids or local radiation); last chemotherapy or radiation must be at least 4 weeks prior to enrollment on this study; patients who decline other potentially curative therapy may be eligible; prior radiation therapy must not have been to more than 25% of the bone marrow; whole pelvic radiation is considered to be over 25% * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * Life expectancy of greater than 12 weeks * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total/…