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

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/direct bilirubin \< 1.5 X institutional upper limit of normal; patients with elevation of indirect (unconjugated) bilirubin alone, as in Gilbert's syndrome, are eligible

Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) \< 2.5 X institutional upper limit of normal

Creatinine =\< institutional upper limit of normal OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal

Prior allogeneic stem cell transplant patients will be allowed to enroll if they are past day +100 of transplant, have no active graft-versus-host-disease, are not on any immunosuppressants and have been off immunosuppressants for at least 4 weeks; prior autologous stem cell transplant patients will also be allowed to enter this study if they are past their day +100 of transplant

Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and 4 months after completion of MLN8237 administration; should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately; men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of MLN8237 administration

Ability to understand and the willingness to sign a written informed consent document

According to current guidelines, patients must be able to take oral medication and to maintain a fast as required for 2 hours before and 1 hour after MLN8237 administration; these guidelines may change pending results from an ongoing food effects study

What this study is about