Lenvatinib in Patients With Previously Treated Advanced Biliary Tract Cancer

Inclusion Criteria: * Inclusion Criteria: 1. Pathologically or cytologically confirmed adenocarcinoma of biliary tract cancer (intrahepatic, extrahepatic cholangiocarcinoma, gall bladder cancer), at least one prior chemotherapy. 2. Participants who received adjuvant chemotherapy are eligible if this therapy was completed and recurrent has not been shown for 6 months after the completion of the therapy 3. Measurable disease meeting the following criteria: At least 1 lesion of ≥ 1.0 cm in the longest diameter for a non-lymph node or ≥ 1.5 cm in the short-axis diameter for a lymph node that is serially measurable according to Response Evaluation Criteria in Solid Tumors 1.1 (RECIST1.1) using computerized tomography/magnetic resonance imaging (CT/MRI). Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must show evidence of progressive disease based on RECIST 1.1 to be deemed a target lesion. 4. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0-1 5. Survival expectation of 3 months or longer after beginning of study treatment 6. Males or females age ≥ 18 years at the time of informed consent 7. All chemotherapy- or radiation-related toxicities must have resolved to Grade 0-1 per Common Terminology Criteria for Adverse Events (CTCAE v 4.03), except alopecia, infertility, and the adverse events listed in inclusion criteria 8. Adequately controlled blood pressure (BP) with or without antihypertensive medications (defined as BP ≤ 150/90 mm Hg at Screening and no change in antihypertensive medications within 1 week prior to the first dose of study drug) 9. Participants with adequate function of major organs and blood coagulation: 10. Absolute neutrophil count (ANC) ≥ 1500/mm\^3 ( ≥ 1.5×103/μl); Platelets ≥ 100,000/mm3 ( ≥ 100×10\^9/L); Hemoglobin ≥ 9.0 g/dL; Bilirubin ≤ 2.0 mg/dL except for unconjugated hyperbilirubinemia or Gilbert's syndrome; Alkaline phosphatase (ALP), aspartate aminotransferase (AST), and alanine aminotransferase (ALT) ≤ 3.0 × upper limit of normal (ULN) ( ≤ 5.0 × ULN for participants with the liver metastasis); Creatinine clearance ≥ 40 mL/min per the Cockcroft and Gault formula; Prothrombin time-International Normalized Ratio (PT-INR) ≤ 1.5; 11. Participants must voluntarily agree to provide written informed consent; 12. Participants must be willing and able to comply with all aspects of the protocol Exclusion Criteria: 1. Ascites of moderate, severe, or requiring drainage 2. Proteinuria of ≥ 2+ on dipstick testing (Grade ≤ 1 confirmed by quantitative assessment is eligible) 3. Gastrointestinal malabsorption or any other condition that in the opinion of the investigator might affect the absorption of study drug 4. New York Heart Association congestive heart failure of class II or above, unstable angina, myocardial infarction, or serious cardiac arrhythmia associated with significant cardiovascular impairment within the past 6 months from the first dose of study drug 5. A prolonged QT/QTc interval (QTcF \> 480 ms) 6. Known to be human immunodeficiency virus (HIV) positive 7. Active infection requiring systemic treatment 8. Bleeding or thrombotic disorders or chronic systemic use of anticoagulants requiring therapeutic INR monitoring, eg, warfarin or similar agents (treatment with low molecular weight heparin is permitted) 9. Gastrointestinal bleeding event or active hemoptysis (bright red blood of at least 0.5 teaspoon) within 21 days prior to the first dose of study drug Active malignancy (except for BTC or definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, carcinoma in-situ of the cervix, or early stage gastric/colorectal cancer) within the past 24 months prior to the first dose of study drug 10. Known intolerance to the study drug or any of the excipients 11. History of drug or alcohol dependency or abuse within the last 24 months prior to the first dose of study drug 12. Any medical or other condition that in the opinion of the investigator(s) would preclude the participant's participation in a clinical study 13. Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive human chorionic gonadotropin \[hCG or B-hCG\]). A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 3 days before the first dose of study drug. 14. For either males unless undergoing a successful vasectomy (confirmed azoospermia) or females of childbearing potential, the participant and his/her partner do not agree to use a medically appropriate method of contraception throughout the entire study period