Inclusion Criteria:

          -  Pathologic findings supporting the clinical impression of anaplastic thyroid
             carcinoma. Diagnosis may include consistent with or suggestive of terminology
             associated with: anaplastic thyroid carcinoma, undifferentiated carcinoma, squamous
             carcinoma; carcinoma with spindled, giant cell, or epithelial features; poorly
             differentiated carcinoma with pleomorphism, extensive necrosis with tumor cells
             present

          -  Patients deemed to have unresectable locoregional disease or metastatic disease.
             Patients who are unwilling to undergo surgery or external beam radiation are also
             eligible. Patients with a BRAFV600E mutation who are unable to receive the Food and
             Drug Administration (FDA) approved drugs, dabrafenib/trametinib, are eligible as long
             as this is documented

          -  Total bilirubin =< 1.5 x upper limit of normal (ULN). Total bilirubin =< 3 x ULN for
             patients with Gilbert's syndrome

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x ULN, (5 x ULN for patients with concurrent liver metastases)

          -  Serum creatinine =< within 1.5 x ULN

          -  Absolute neutrophil count (ANC) >= 1.0 x 10^9/L

          -  Platelets >= 100 x 10^9/L

          -  For patients receiving therapeutic anticoagulation: stable anticoagulant regimen and
             stable institutional normalized ratio (INR) during the 28 days immediately preceding
             initiation of study treatment

          -  Subjects must be willing to undergo tumor biopsy prior to and after treatment with
             lenvatinib/pembrolizumab, unless in the opinion of the treating physician, a biopsy is
             not feasible or safe

          -  Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
             Evaluation of ECOG is to be performed within 7 days prior to the date of
             allocation/randomization

          -  The participant (or legally acceptable representative if applicable) provides written
             informed consent for the trial

          -  A male participant must agree to use a contraception during the treatment period and
             for at least 8 months after the last dose of study treatment and refrain from donating
             sperm during this period

          -  A female participant is eligible to participate if she is not pregnant, not
             breastfeeding, and at least one of the following conditions applies: a.) Not a woman
             of childbearing potential (WOCBP) OR b.) A WOCBP who agrees to follow the
             contraceptive guidance during the treatment period and for at least 6 months after the
             last dose of study treatment

        Exclusion Criteria:

          -  Uncontrolled blood pressure (systolic blood pressure [BP] > 140 mmHg or diastolic BP >
             90 mmHg) in spite of an optimized regimen of antihypertensive medication

          -  Electrolyte abnormalities that have not been corrected, with the exception of calcium
             if oral calcium and calcitriol are being titrated

          -  Significant cardiovascular impairment: history of congestive heart failure greater
             than New York Heart Association (NYHA) class II, unstable angina, myocardial
             infarction or stroke within 6 months of the first dose of study drug, or cardiac
             arrhythmia requiring medical treatment at screening

          -  Patients with clinically significant hemoptysis or tumor bleeding within two weeks
             prior to first dose of targeted therapy. Patients with suspected tracheal or
             esophageal invasion can be included on a case-by-case basis after a discussion with
             the principal investigator. The degree of tumor invasion/infiltration of major blood
             vessels (e.g. carotid artery) should be considered because of the potential risk of
             severe hemorrhage and tracheoesophageal fistula associated with tumor
             shrinkage/necrosis following lenvatinib therapy

          -  Major surgery within 1 week of course 1 day 1

          -  Patients with open wounds or fistulas are excluded

          -  Subjects having > 2+ proteinuria on urine dipstick testing unless a 24-hour urine
             collection for quantitative assessment indicates that the urine protein is < 1 g/24
             hours

          -  Untreated brain metastases

          -  Prior chemotherapy within < 1 week prior to study day 1 or patients who have not
             recovered (i.e., =< grade 2) from adverse events due to a previously administered
             agent

          -  Previous anti-angiogenic targeted therapy is excluded

          -  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

          -  History of human immunodeficiency virus (HIV) or active hepatitis B (chronic or acute)
             or hepatitis C infection. Patients with past or resolved hepatitis B infection
             (defined as having a negative hepatitis B surface antigen [HBsAg] test and a positive
             anti-HBc [antibody to hepatitis B core antigen] antibody test) are eligible. However,
             patients with past or resolved HBV should be monitored for reactivation by a
             specialist. Patients positive for hepatitis C virus (HCV) antibody are eligible only
             if polymerase chain reaction (PCR) is negative for HCV ribonucleic acid (RNA)

          -  Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy
             (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of
             immunosuppressive therapy within 7 days prior to the first dose of study drug

          -  Has received a live vaccine within 30 days prior to the first dose of study drug.
             Examples of live vaccines include, but are not limited to, the following: measles,
             mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus
             Calmette-Guerin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection
             are generally killed virus vaccines and are allowed; however, intranasal influenza
             vaccines (e.g., FluMist) are live attenuated vaccines and are not allowed

          -  Has severe hypersensitivity (>= grade 3) to pembrolizumab and/or any of its excipients

          -  Has a history of (non-infectious) pneumonitis that required steroids or has current
             pneumonitis

          -  Has known psychiatric or substance abuse disorders that would interfere with
             cooperation with the requirements of the trial

          -  Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a
             positive beta-human chorionic gonadotropin [beta-hCG] (or human chorionic gonadotropin
             [hCG]) test with a minimum sensitivity of 25 IU/L or equivalent units of beta-hCG [or
             hCG]). A women of childbearing potential (WOCBP) who has a positive urine pregnancy
             test within 72 hours prior to the first infusion will be excluded. If the urine test
             is positive or cannot be confirmed as negative, a serum pregnancy test will be
             required