Inclusion Criteria:

          -  Willing and able to provide written informed consent/assent for the trial.

          -  Be ≥ 18 years of age on day of signing informed consent.

          -  Have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST)
             1.1.

          -  Have archival tissue where available. Those participants enrolled on the phase 1
             escalation trial where archival tissue is not available will undergo a fresh biopsy
             where clinically feasible after discussion with the sponsor.

          -  In addition, participants enrolled on the phase 1 dose escalation, phase 1 expansion
             or Phase II trial must be willing and able to provide tissue from a newly obtained
             core or excisional biopsy of a tumor lesion.

          -  Randomized Phase II: Tumor proportional score of PD-L1 ≥1%.

          -  Have a performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG)
             Performance Scale.

          -  Demonstrate adequate organ function.

          -  Have a histologic or cytologic diagnosis of Stage IV non-small cell lung cancer
             (NSCLC).

          -  Phase I/IB (Pre-treated): Have progression from at least one prior line of therapy.
             Maintenance therapy following platinum doublet-based chemotherapy is not considered as
             a separate regimen of therapy. Participants who received platinum-containing adjuvant,
             neoadjuvant or definitive chemoradiation therapy given for locally advanced disease,
             and developed recurrent (local or metastatic) disease within 6 months of completing
             therapy are eligible for these arms. Participants with recurrent disease ≥ 6 months
             after completing a platinum-containing adjuvant, neoadjuvant or definitive
             chemoradiation therapy given for locally advanced disease, who also subsequently
             progressed during or after a systemic regimen given to treat the recurrence, must have
             received another treatment in the first-line metastatic setting.

          -  Randomized Phase II: Be treatment naïve in the stage IV setting, with the exception of
             participants whose tumors harbor an activation mutation (including but not limited to
             EGFR, ALK, ROS1) and were previously treated with targeted therapy. Participants who
             received platinum-containing adjuvant, neoadjuvant or definitive chemoradiation
             therapy given for locally advanced disease, and developed recurrent (local or
             metastatic) disease < 6 months of completing therapy are ineligible for this arm.
             Subjects with recurrent disease ≥ 6 months after completing a platinum-containing
             adjuvant, neoadjuvant or definitive chemoradiation therapy given for locally advanced
             disease, who also subsequently progressed during or after a systemic regimen given to
             treat the recurrence, are eligible for this arm.

          -  Females of childbearing potential should be willing to use 2 methods of birth control
             or be surgically sterile, or abstain from heterosexual activity for the course of the
             study through 120 days after the last dose of study medication.

          -  Males should agree to use an adequate method of barrier contraception starting with
             the first dose of study therapy through 120 days after the last dose of study therapy.

        Exclusion Criteria:

          -  Is currently participating in and receiving study therapy or has participated in a
             study of an investigational agent and received study therapy or used an
             investigational device within 4 weeks of the first dose of treatment.

          -  Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at doses
             ≥ 10 mg prednisone or any other form of systemic immunosuppressive therapy within 7
             days prior to the first dose of trial treatment. Participants are permitted to use
             topical, ocular, intra-articular, intranasal, and inhalational corticosteroids (with
             minimal systemic absorption). Physiologic replacement doses of systemic
             corticosteroids are permitted, even if >= 10 mg/day prednisone equivalents. A brief
             course (≤28 days) of corticosteroids for prophylaxis (e.g., contrast dye allergy) or
             for treatment of non-autoimmune conditions (e.g., delayed-type hypersensitivity
             reaction caused by contact allergen) is permitted.

          -  Has a known history of tuberculosis (TB) Disease (Mycobacterium tuberculosis).

          -  Hypersensitivity to pembrolizumab, vorinostat or any of its excipients.

          -  Participants enrolled on the phase II randomized trial, who have had prior treatment
             with a PD1 or PDL1 inhibitor, anti-CTLA 4 antibody or any other antibody or drug that
             specifically targets immune checkpoint pathway (i.e. not "immune therapy naïve").
             -Note: For those enrolled in the phase I dose escalation, prior use of a PD1 or PDL1,
             anti-CTLA4 antibody or any other antibody or drug that specifically targets immune
             checkpoint pathway is allowed. For those enrolled in the phase IB, prior use of a PD1
             or PDL1, anti-CTLA4 antibody or any other antibody or drug that specifically targets
             immune checkpoint pathway is required. For all participants in all phases, prior use
             of a vaccine for treatment of cancer is allowed.

          -  Participants enrolled in the phase Ib expansion who have never previously been treated
             with a PD1 or PDL1 inhibitor, anti-CTLA 4 antibody or any other antibody or drug that
             specifically targets immune checkpoint pathway in the past (i.e. not "pre-treated").

          -  Participants who have received thoracic radiation >30Gy within 6 months of the first
             dose of pembrolizumab.

          -  Patients taking any HDACi other than vorinostat.

          -  Has had a prior anti-cancer monoclonal antibody (mAb) within 4 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 4 weeks earlier.

          -  Has had prior chemotherapy with 3 weeks, or 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: Patients with ≤ Grade 2 neuropathy are an exception to this criterion and may
             qualify for the study. Note: Patients with any grade alopecia are an exception to this
             criterion and may qualify for the study.

          -  If participant received major surgery, they must have recovered adequately from the
             toxicity and/or complications from the intervention prior to starting therapy.

          -  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) metastases and/or carcinomatous
             meningitis. Previously treated brain metastases may be an exception if stable and
             specific other criteria are met.

          -  Has active autoimmune disease that has required systemic treatment in the past 2
             years. Replacement therapy is not considered a form of systemic treatment. Patients
             are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual
             hypothyroidism due to autoimmune condition only requiring hormone replacement,
             psoriasis not requiring systemic treatment, or conditions not expected to recur in the
             absence of an external trigger.

          -  Has an active infection requiring systemic therapy.

          -  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., HBsAg reactive) or Hepatitis C (e.g., HCV 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.

          -  Has a history of, or any evidence of active non-infectious pneumonitis that required
             or requires steroids.

          -  Has evidence of interstitial lung disease

          -  Has a history of symptomatic (NYHA class II-IV) heart failure