Pembrolizumab and Vorinostat in Patients With Relapsed or Refractory DLBCL, FCL or HL.

Inclusion Criteria:

* Have a histologically confirmed diagnosis of follicular lymphoma, diffuse large B-cell lymphoma, or classical Hodgkin lymphoma according to the World Health Organization (WHO) classification, with hematopathology review at the participating institution

  * FL: grade 1, 2, 3A, or 3B are eligible
  * DBLCL: transformed indolent lymphomas (TIL), primary mediastinal large B-cell lymphoma (PMBCL), and aggressive B-cell lymphoma unclassified (BCL-U) are eligible
  * HL: all classical HL subtypes are eligible except for nodular lymphocyte predominant Hodgkin lymphoma, which is excluded
* Patients with HL or DLBCL must refuse or not be candidates for curative autologous stem cell transplantation
* Have relapsed or refractory disease after at least 1 prior regimen, including:

  * Recurrence of disease after a documented complete response (CR)
  * Progression of disease after a partial response (PR) to the prior regimen
  * Partial response (PR), stable disease (SD) or progressive disease (PD) at the completion of the prior treatment regimen; if a patient has PR to prior regimen without PD, there must be biopsy-proven residual disease that is measurable
* Documented informed consent of the participant or legally authorized representative
* Have measurable disease by computed tomography (CT) or positron emission tomography (PET) scan, with one or more sites of disease \>= 1.5 cm in longest dimension
* Be willing to provide tissue from a newly obtained core or excisional biopsy of a tumor lesion prior to starting study therapy or from archival tissue of a biopsy that was performed after the most recent systemic therapy
* Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) performance scale
* Absolute neutrophil count (ANC) \>= 1,000/mcL (within 14 days of treatment initiation)
* Platelets \>= 75,000/mcL (within 14 days of treatment initiation)
* Hemoglobin \>= 8 g/dL without transfusion or erythropoietin (EPO) dependency (within 7 days of assessment (within 14 days of treatment initiation)
* Serum creatinine =\< 1.5 x upper limit of normal (ULN) OR measured or calculated creatinine clearance (glomerular filtration rate \[GFR\] can also be used in place of creatinine or creatinine clearance (CrCl) \>= 60 mL/min for subject with creatinine levels \> 1.5 x institutional ULN (within 14 days of treatment initiation)
* Serum total bilirubin =\< 1.5 x ULN or =\< 3 x ULN if patient has Gilberts disease OR direct bilirubin =\< ULN for subjects with total bilirubin levels \> 1.5 ULN (within 14 days of treatment initiation)
* Aspartate aminotransferase (AST) serum glutamic-oxaloacetic transaminase (SGOT) and alanine aminotransferase (ALT) serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x ULN OR =\< 5 x ULN for subjects with liver involvement by lymphoma as the etiology of transaminase elevation (within 14 days of treatment initiation)
* Albumin \>= 2.5 mg/dL (within 14 days of treatment initiation)
* International normalized ratio (INR) or prothrombin time (PT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or partial thromboplastin time (PTT) is within therapeutic range of intended use of anticoagulants (within 14 days of treatment initiation)
* Activated partial thromboplastin time (aPTT) =\< 1.5 x ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants (within 14 days of treatment initiation)
* Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication; if the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Female subjects of childbearing potential must be willing to use an adequate method of contraception for the course of the study through 120 days after the last dose of study medication; Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject
* Male subjects of childbearing potential must agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy; Note: abstinence is acceptable if this is the usual lifestyle and preferred contraception for the subject

Exclusion Criteria:

* Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 3 weeks of the first dose of treatment
* Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment
* Has received a prior allogeneic hematopoietic stem cell transplant within the past 5 years, requires immunosuppression, or has evidence of active graft-versus-host-disease
* Has received prior autologous hematopoietic stem cell transplant within the last 60 days
* Has a known history of active TB (Bacillus tuberculosis)
* Severe hypersensitivity to pembrolizumab or any of its excipients
* Has had a prior anti-cancer monoclonal antibody (mAb) within 3 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to agents administered more than 3 weeks earlier; if a patient has progressive or stable disease to prior regimen, rituximab is allowed up to 2 weeks prior to the initiation of study therapy
* Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study day 1 or who has not recovered (i.e., =\< grade 1 or at baseline) from adverse events due to a previously administered agent; Note: subjects with =\< grade 2 neuropathy are an exception to this criterion and may qualify for the study; Note: if subject received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy
* Has taken valproic acid, or another histone deacetylase inhibitor, within 2 weeks prior to study day 1
* Has a known additional malignancy that is progressing or requires active treatment; exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer
* 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
* Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs); replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment; a history of hemolytic anemia associated with the lymphoma does not exclude a patient from the study
* Has a history of (non-infectious) pneumonitis that required steroids or current pneumonitis
* Has an active infection requiring systemic therapy
* Has a QT interval corrected for heart rate (QTc) \> 470 ms using the Fridericia formula; if the screening electrocardiogram (ECG) has a QTc \> 470ms, the mean QTc of 3 electrocardiograms (ECGs) can be utilized, but must be \< 470 ms
* Is unable to swallow capsules, has a partial or small bowel obstruction, or has a gastrointestinal condition resulting in a malabsorptive syndrome (e.g. small bowel resection with malabsorption)
* Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator
* Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial
* Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment
* Has a known history of human immunodeficiency virus (HIV) (HIV 1/2 antibodies)
* Has known active hepatitis B (e.g., hepatitis B surface antigen \[HBsAg\] reactive) or hepatitis C (e.g., hepatitis C virus \[HCV\] ribonucleic acid \[RNA\] \[qualitative\] is detected)
* Has received a live vaccine within 30 days of planned start of study therapy; Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed