Inclusion Criteria:

          -  Be 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 the Lugano Criteria

          -  Phase I: patient must have histologically confirmed relapsed or refractory Peripheral
             T-cell lymphoma (PTCL) or cutaneous T-cell Lymphoma (PTCL) as per World Health
             Organization (WHO) criteria. Expansion phase: patients must have histologically
             confirmed relapsed or refractory PTCL, relapsed or refractory CTCL, de novo PTCL, de
             novo tumor stage mycosis fungoides (excluding de novo plaque and patches CTCL) as per
             WHO criteria.

          -  There is no upper limit for the number of prior therapies. Patient may have relapsed
             after prior autologous stem cell transplant.

          -  Be willing to provide tissue from a newly obtained core or excisional biopsy of a
             tumor lesion. Be willing to provide fine-needle aspiration (FNA) of a tumor lesion.
             Newly-obtained is defined as a specimen obtained up to 6 weeks (42 days) prior to
             initiation of treatment on Day 1. Subjects for whom newly-obtained samples cannot be
             provided (e.g. inaccessible or subject safety concern) may submit an archived specimen
             only upon agreement from the Sponsor.

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

          -  Demonstrate adequate organ function, all screening labs should be performed within 10
             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 - 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 - Contraception, starting with the first dose of study therapy through
             120 days after the last dose of study therapy.

        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 4 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 a known history of active Bacillus Tuberculosis (TB)

          -  Hypersensitivity to pralatrexate, or decitabine or pembrolizumab or any of its
             excipients.

          -  Has received prior allogeneic stem cell transplant.

          -  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, 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 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. Subjects with previously treated brain metastases may participate provided
             they are stable (without evidence of progression by imaging for at least four weeks
             prior to the first dose of trial treatment and any neurologic symptoms have returned
             to baseline), have no evidence of new or enlarging brain metastases, and are not using
             steroids for at least 7 days prior to trial treatment. This exception does not include
             carcinomatous meningitis which is excluded regardless of clinical stability.

          -  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.

          -  Has known history of, or any evidence of active, non-infectious pneumonitis.

          -  Has an active infection requiring systemic therapy.

          -  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 received prior therapy with an anti-PD-1, anti-programmed death (PD)-L1, or
             anti-PD-L2 agent.

          -  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 (HCV) (e.g., HCV
             RNA [qualitative] is detected).

          -  Has received a live vaccine within 30 days of planned start of study therapy.