Study of the Safety and Activity of Lenvatinib (E7080) in Subjects With KIF5B-RET-Positive Adenocarcinoma of the Lung

Inclusion Criteria: 1. Subjects must have a cytological or histological confirmed diagnosis of adenocarcinoma of the lung. 2. Subject must be known to be RET positive (known KIF5B-RET translocation, or other confirmed RET translocations (e.g., CCDC6-RET)) or have an available tumor sample for local or central testing obtained prior to consent (Screen 1). Subjects whose samples need to be submitted for central laboratory testing must be current non-smokers and not known to have mutation in EGFR, KRAS, or ALK. 3. Subjects may have received up to three prior systemic anticancer treatment regimens for adenocarcinoma of the lung (including adjuvant therapies and tyrosine-kinase inhibitors \[TKI\]), unless discussed with the sponsor. 4. Subjects must have a clinically indicated need for systemic chemotherapy for adenocarcinoma of the lung based on the investigator's assessment 5. Presence of measurable disease meeting the following criteria: 1. At least one lesion of at least 1.0 cm in the long-axis diameter for a non-lymph node or at least 1.5 cm in the short-axis diameter for a lymph node which is serially measurable according to Response Evaluation Criteria in Solid Tumors 1.1 (RECIST 1.1) using either computerized tomography (CT) or magnetic resonance imaging (MRI). If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of at least 1.5 cm. 2. Lesions previously treated with radiotherapy or locoregional therapy must show radiographic evidence of disease progression to be deemed a target lesion. 6. Subjects with known brain metastases who have completed whole brain radiotherapy, stereotactic radiosurgery, or complete surgical resection will be eligible if they have remained clinically stable, asymptomatic and off of steroids for 28 days. 7. Adequate bone marrow function, defined as: 1. Absolute neutrophil count (ANC) greater than or equal to 1.5 x 10\^9/L (greater than or equal to 1500/mm\^3) 2. Hemoglobin (Hb) greater than or equal 8.5 g/dL 3. Platelet count greater than or equal 75 x 10\^9/L (greater than or equal 75,000/mm\^3) 8. Adequate liver function, defined as: 1. Bilirubin less than or equal 1.5 x upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome 2. Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) less than or equal 3 x ULN (less than or equal 5 x ULN if subject has liver metastases). If alkaline phosphatase is greater than 3 x ULN (in absence of liver metastases) or greater than 5 x ULN (in presence of liver metastases) AND the subject also is known to have bone metastases, the liver-specific alkaline phosphatase must be separated from the total and used to assess the liver function instead of total alkaline phosphatase. 9. Adequate renal function, defined as calculated creatinine clearance greater than 40 mL/min per the Cockcroft and Gault formula. 10. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP less than 150/90 mmHg at screening and no change in antihypertensive medications within 1 week before Cycle 1/Day 1 (C1D1). 11. Eastern Cooperative Oncology Group (ECOG)-Performance Status (PS) of 0 or 1. 12. Survival expectation of 12 weeks or longer after starting study drug. 13. Males or females aged at least 18 years (or any age greater than 18 years as determined by country legislation) at the time of informed consent (Screen 1). 14. Females must not be breast-feeding or pregnant at Screening or Baseline (as documented by a negative beta-human chorionic gonadotropin \[B-hCG\] test with a minimum sensitivity of 25 IU/L or equivalent units of B-hCG). A separate baseline assessment is required if a negative Screening pregnancy test was obtained more than 72 hours before the first dose of study drug. 15. All females will be considered to be of childbearing potential unless they are postmenopausal (amenorrheic for at least 12 consecutive months, in the appropriate age group and without other known or suspected cause) or have been sterilized surgically (i.e., bilateral tubal ligation, total hysterectomy or bilateral oophorectomy, all with surgery at least one month before dosing). 16. Females of childbearing potential must not have had unprotected sexual intercourse within 30 days before study entry and must agree to use a highly effective method of contraception (e.g., total abstinence, an intrauterine device, a double-barrier method \[such as condom plus diaphragm with spermicide\], a contraceptive implant, an oral contraceptive, or have a vasectomized partner with confirmed azoospermia) throughout the entire study period and for 30 days after study drug discontinuation. If currently abstinent, the subject must agree to use a double barrier method as described above if she becomes sexually active during the study period or for 30 days after study drug discontinuation. Females who are using hormonal contraceptives must have been on a stable dose of the same hormonal contraceptive product for at least 4 weeks before dosing and must continue to use the same contraceptive during the study and for 30 days after study drug discontinuation. 17. Male subjects must have had a successful vasectomy (confirmed azoospermia) or they and their female partners must meet the criteria above (i.e., not of childbearing potential or practicing highly effective contraception throughout the study period and for 30 days after study drug discontinuation). No sperm donation is allowed during the study period and for 30 days after study drug discontinuation. 18. Provide written informed consent (Screen 1 and Screen 2) 19. Willing and able to comply with all aspects of the protocol Exclusion Criteria: 1. Subjects who have received any anticancer therapy (including surgery, locoregional, biological, immunotherapy, hormonal, or radiotherapy) within 21 days before the first dose of study drug (28 days for investigational therapies). 2. Leptomeningeal metastases or brain metastases except as for Inclusion Criterion #6. 3. Subjects who have not recovered from toxicities as a result of prior anticancer therapy to less than Grade 2 severity per the National Cancer Institute Common Terminology Criteria for Adverse Events (CTCAE) v4.0, except alopecia and infertility. 4. 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. 5. Gastrointestinal malabsorption or any other condition in the opinion of the investigator that might affect the absorption of lenvatinib. 6. Active malignancy (except for adenocarcinoma of the lung or definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix) within the past 24months. 7. Major surgery within 3 weeks before the first dose of study drug. 8. Bleeding or thrombotic disorders or use of anticoagulants such as warfarin or similar agents requiring therapeutic international normalized ratio (INR) monitoring. (Treatment with low molecular weight heparin is allowed.) 9. Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks before the first dose of study drug. 10. Active infection (any infection requiring treatment). 11. Symptomatic central nervous system (CNS) disease. 12. Subjects having greater than 1+ proteinuria on urine dipstick testing will undergo 24-hour urine collection for quantitative assessment of proteinuria. Subjects with urine protein greater than or equal to 1 g/24-hour will be ineligible. 13. Any medical or other condition that in the opinion of the investigator(s) would preclude the subject's participation in a clinical study or would preclude them from completing the study. 14. Scheduled for surgery during the study.