Inclusion Criteria:

          -  Diagnosis/Condition for entry into the trial: Metastatic well differentiated
             neuroendocrine tumors of primary lung, thymic, small bowel and colorectal origin
             (including unknown primary)

          -  Evidence of radiographic disease progression with scan documenting progression
             occurring within 8 months of signing informed consent

          -  At least two prior lines of systemic treatment. If the only prior line of treatment
             was adjuvant or neoadjuvant, patient must have completed treatment within 12 months.
             There is no limit to number of prior therapies.

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

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

          -  Demonstrate adequate organ function and laboratory values. All screening labs should
             be performed within 14 days of treatment initiation.

          -  Females of childbearing potential (FOCBP) should have a negative serum pregnancy
             within 72 hours prior to receiving the first dose of study medication.

          -  FOCBP must agree to use adequate contraception as outlined in study documentation for
             the course of the through 120 days after the last dose of study medication.

          -  Male participants of childbearing potential must agree to use an adequate method of
             contraception as outlined in study documentation, starting with the first dose of
             study therapy through 120 days after the last dose of study therapy.

        Exclusion Criteria:

          -  Poorly differentiated neuroendocrine carcinoma

          -  Pancreatic neuroendocrine tumor

          -  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.

          -  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.

          -  Known history of active TB (Bacillus Tuberculosis)

          -  Hypersensitivity to pembrolizumab or any of its excipients.

          -  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:
             Potential participants with ≤ Grade 2 neuropathy are an exception to this criterion
             and may qualify for the study. Note: If have received major surgery within 3 weeks,
             must have recovered adequately from the toxicity and/or complications from the
             intervention prior to starting therapy. Adequate wound healing after major surgery
             must be assessed clinically, independent of time elapsed for eligibility.

          -  Serious non-healing wound, ulcer or bone fracture

          -  Has pre-existing >/= Grade 3 gastrointestinal (GI) or non-GI fistula

          -  Has significant cardiovascular impairment within 12 months of the first dose of study
             drug

          -  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.

          -  Known active central nervous system (CNS) metastases and/or carcinomatous meningitis.
             Potential participants 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. Replacement therapy is not considered a form of systemic treatment.

          -  History of (non-infectious) pneumonitis that required steroids, or current
             pneumonitis.

          -  An active infection requiring systemic therapy.

          -  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.

          -  Known psychiatric or substance abuse disorders that would interfere with cooperation
             with the requirements of the trial.

          -  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-PD-L1, or anti-PD-L2 agent.

          -  Has received prior therapy with a tyrosine kinase inhibitor (TKI) (e.g.; sunitinib,
             pazopanib, cabozantinib)

          -  Known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).

          -  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.

          -  Uncontrolled hypertension defined as systolic blood pressure >150 mmHg or diastolic
             pressure >90 mmHg, despite optimal medical management

          -  Thrombotic or embolic events such as a cerebrovascular accident including transient
             ischemic, attacks, DVT within the past 6 months

          -  Bleeding or thrombotic disorders or use of anticoagulants, such as warfarin, or
             similar agents requiring therapeutic international normalized ration (INR)
             monitoring.(Treatment with low molecular weight heparin (LMWH) is allowed)

          -  Marked baseline prolongation of QT/QTc interval (QTc interval ≥ 480 msec) using the
             Fridericia method (QTc = QT/RR0.33) for QTc analysis

          -  Clinically significant bleeding within 4 weeks

          -  Medical need for the continued use of potent inhibitors/inducers of CYP3A4

          -  Creatinine clearance <30 mL/min

          -  Any condition that impairs patient's ability to swallow whole pills or
             gastrointestinal malabsorption that, in the investigator's opinion, might affect
             absorption of lenvatinib