Lenvatinib and Pembrolizumab for the Treatment of Stage IVB Locally Advanced and Unresectable or Stage IVC Metastatic Anaplastic Thyroid Cancer

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 * Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/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 * Sub…