Inclusion Criteria

• Must have histological diagnosis consistent of Anaplastic Thyroid Cancer
• Cytologic diagnosis by fine needle aspiration alone is not sufficient
  • Histologic diagnosis may be made by core needle biopsy, incisional biopsy, thyroidectomy, or other surgical biopsy
  • Fresh tumor biopsies (re-biopsy) should be obtained whenever feasible
• Central pathology review may take place prior to or after  start of treatment with lenvatinib
  • Central review of pathology is required for study participation, but not required prior to enrollment or start of treatment in order to avoid delay
  • If results of central pathology review are not available prior to the start of study treatment, the confirmation of diagnosis of ATC at the local laboratory is mandatory prior to scheduled start of treatment with lenvatinib
  • If central pathology review indicates a diagnosis other than ATC, treatment with lenvatinib may continue per standard of care, at the discretion of the treating investigator
  • Other diagnoses will be taken off this study and replaced for the purpose of efficacy analyses
• Has differentiated thyroid carcinoma (DTC) with focus loci of ATC
  • If pathology showing a small focus of ATC arising out of DTC and the measurable disease is not fully consistent with ATC, confirmation of ATC by biopsy is required
• Has an incidental focus of medullary thyroid cancer (MTC), DTC, and/or poorly differentiated thyroid cancer in ATC
• Histological diagnosis of ATC made through surgical resection
• Has had prior neoadjuvant, adjuvant, or palliative chemotherapy for ATC
• Has measurable disease based on investigator's assessments meeting the following criteria
  • At least 1 lesion of ≥ 10 millimeters (mm) in the longest diameter for a non-lymph node 
  • ≥ 15 mm in the short-axis diameter for a lymph node which is serially measurable
    • According to Response Evaluation Criteria In Solid Tumors (RECIST) 1.1 using computerized tomography (CT) or magnetic resonance imaging (MRI)
  • Lesions that have had external beam radiotherapy or locoregional therapies such as radiofrequency ablation must show evidence of subsequent progressive disease (substantial size increase of ≥ 20%) to be deemed a target lesion
• Known brain metastases after completed whole brain radiotherapy, stereotactic radiosurgery, or complete surgical resection if remain clinically stable, asymptomatic, and off steroids for 1 month prior to enrollment
• All previous chemotherapy or radiation therapy-related toxicities, except dry mouth, dysphagia, esophagitis, mucositis, alopecia, and irreversible late sequelae of radiation therapy, must have resolved to Grade 0 or 1 per Common Terminology Criteria for Adverse Events (CTCAE v 4.03)
• All wounds from prior surgery must have adequately recovered
• Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
• Blood pressure (BP) ≤ 140/90 mmHg at screening with or without antihypertensive medications and no change in antihypertensive medications within 1 week prior to cycle 1/day 1
• Adequate renal function as evidenced by calculated creatinine clearance ≥ 30 mL/min according to the Cockcroft and Gault formula
• Adequate bone marrow function
  • Absolute neutrophil count ≥ 1.5 x 10^9/L
  • Hemoglobin ≥ 9.0 g/dL (can be corrected by growth factor or transfusion)
  • Platelet count ≥ 100 x 10^9/L
• Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) ≤ 1.5
• Adequate liver function
  • Bilirubin ≤ 1.5 x upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome
  • Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) ≤ 3 x ULN (≤ 5 x ULN if participant has liver metastases)
  • If ALP is > 3 x ULN (in the absence of liver metastases) or > 5 x ULN (in the presence of liver metastases) and also has bone metastases, the liver-specific ALP must be separated from the total and used to assess the liver function instead of the total ALP
• Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol

Exclusion Criteria

• Has differentiated thyroid cancer (DTC) or MTC
  • However, ATC arising out of DTC is allowed, as long as the measurable disease is clinically consistent with ATC i.e., rapidly progressive and/or 18F fluorodeoxyglucose (FDG)-avid
• Newly diagnosed patients who are considered appropriate candidates for comprehensive multimodality treatment (involving surgery and/or external beam radiotherapy or chemo radiotherapy)
• Prior treatment with lenvatinib or any tyrosine kinase inhibitor (TKI) 
  • Except for combination therapy of radiation and reduced dose of TKI given for the purpose of radiosensitization
• Major surgery within 2 weeks prior to the first dose of lenvatinib
• Has had any anti-cancer treatment within 14 days 
• Has had any investigational agent within 30 days before the first dose of study drug
• Radiotherapy within 3 weeks prior to the first dose of lenvatinib
• Urine protein ≥ 1 gram/24 hours 
  • > 1 proteinuria on urine dipstick testing requires 24 hour urine collection for quantitative assessment of proteinuria
• Significant cardiovascular impairment with history of
  • Congestive heart failure greater than New York Heart Association (NYHA) Class II
  • Unstable angina
  • Myocardial infarction
  • Stroke
  • Cardiac arrhythmia associated with impairment within 6 months of the first dose of study drug
• A clinically significant electrocardiogram (ECG) abnormality, including a marked baseline prolonged QT/QTc interval, e.g., a repeated demonstration of a QTc interval >500 milliseconds (msec)
• Active infection requiring systemic therapy
• Clinically significant hemoptysis or tumor bleeding within two weeks prior to first dose of lenvatinib
• Radiographic evidence of major blood vessel invasion/infiltration
• Other active malignancy except definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or bladder within past 24 months
• Scheduled for major surgery during the study
• Females who are breastfeeding or pregnant at screening or baseline (as documented by a positive beta-human chorionic gonadotropin [ß-hCG] or human chorionic gonadotropin [hCG] test with a minimum sensitivity of 25 international units/liter (IU/L) or equivalent units of ß-hCG [or 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

1. Females of childbearing potential who: (NOTE: 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 1 month before dosing]). For sites outside of the European Union (EU), it is permissible that if a highly effective method of contraception is not appropriate or acceptable to the subject, then the subject must agree to use a medically acceptable method of contraception, i.e. double barrier methods of contraception such as condom plus diaphragm or cervical/vault cap with spermicide.
   1. Do not agree to use a highly effective method of contraception (ie, total abstinence, [if it is their preferred and usual lifestyle], an intrauterine device or intrauterine system, a contraceptive implant, an oral contraceptive, or have a vasectomized partner with confirmed azoospermia) within 30 days before study entry and throughout the entire study period and for 30 days after study drug discontinuation.
   2. Are currently totally abstinent (as their preferred and usual lifestyle), and who do not agree to be totally abstinent during the study period and for 30 days after study drug discontinuation.
   3. Are using hormonal contraceptives but are not on a stable dose of the same hormonal contraceptive product for at least 4 weeks before dosing and who do not agree to use the same contraceptive during the study and for 30 days after study drug discontinuation.
   4. Are using oral hormonal contraceptives and who do not agree to add a barrier method.
2. Evidence of clinically significant disease (e.g., cardiovascular, respiratory, gastrointestinal, renal disease) that in the opinion of the investigator(s) could affect the participant's safety or interfere with the study assessments.
3. Known intolerance to the study drug or any of the excipients.
4. Any medical or other condition that in the opinion of the investigator(s) would preclude the participant's participation in a clinical study.