A Study to Evaluate the Safety and Efficacy of Lenvatinib in Participants With Refractory Differentiated Thyroid Cancer

Inclusion Criteria: 1. Males and females who are diagnosed with locally Recurrent or Metastatic, Progressive, Radioiodine Refractory DTC, Lenvatinib naive and able to provide written informed consent. 2. Histologically or cytologically confirmed diagnosis of one of the following DTC subtypes: Papillary thyroid cancer (PTC) (including the follicular variants and other variants), Follicular thyroid cancer (FTC) (including Hurthle cell, Clear cell and Insular subtypes). 3. Measurable disease meeting the following criteria: i) At least 1 lesion \>= 1.0 centimeter (cm) in the longest diameter for a non-lymph node or \>= 1.5 cm in the short-axis diameter for a lymph node which is serially measurable according to RECIST 1.1 using computerized tomography/magnetic resonance imaging (CT/MRI). ii) Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must have shown evidence of PD based on RECIST 1.1 to be deemed a target lesion. 4. Evidence of disease progression within 12 months of screening scan. 5. Require thyroxine suppression therapy and thyroid stimulating hormone (TSH) should not be elevated (TSH should be less than \[\<\] 4.0 milli-international units per liter \[mIU/L\]). 6. Participant must be radioiodine-refractory or resistant within 12 months of radioiodine therapy and have one of the following: * One or more measurable lesions that do not demonstrate iodine uptake on any radioiodine scan. * One or more measurable lesions that have substantially increased in size within 12 months of radioiodine therapy, despite demonstration of radioiodine activity at the time of that treatment by pre- or post-treatment scanning. * Cumulative activity of radioiodine of greater than (\>) 600 milliecurie (mCi) or 22 gigabecquerels (GBq), with the last dose administered at least 6 months prior to study entry. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. 8. Based on following laboratory assessment: * Creatinine clearance \>= 30 milliliter per minute (mL/min) according to the Cockcroft and Gault formula. * Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) less than or equal to (\<=) 1.5. * Adequate bone marrow function: i. Absolute neutrophil count (ANC) \>=1.5\*10\^9/liter (L) ii. Hemoglobin \>= 9.0 gram per deciliter (g/dL) (can be corrected by growth factor or transfusion) iii. Platelet count \>=100 \* 10\^9/L * Adequate liver function: i. Bilirubin \<= 1.5\*upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome. ii. Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) \<= 3\*ULN (\<= 5\*ULN if participant has liver metastases). If ALP is \> 3\*ULN (in the absence of liver metastases) or \> 5\*ULN (in the presence of liver metastases) and participants are also known to have bone metastases, the liver-specific ALP must be separated from the total and used to assess the liver function instead of the total ALP. 9. Urine dipstick proteinuria should be \< 2+. If \> or equal 2 gram (g) proteinuria is detected with dipstick, a 24-hour period urine test will be performed and the result should be \< or equal to 1 g/24 hours to permit the inclusion of the patient in the clinical trial. 10. Females of childbearing potential must not have had unprotected sexual intercourse within 30 days before program entry and must agree to use a highly effective method of contraception (example, 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 program. * If currently abstinent, participants must agree to use a double-barrier method as described above if they become 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. Exclusion Criteria: 1. Anaplastic or medullary carcinoma of the thyroid. 2. Two or more prior vascular endothelial growth factor (VEGF)/vascular endothelial growth factor receptor (VEGFR)-targeted therapies or any ongoing treatment for iodine-131 (131I) refractory DTC other than TSH-suppressive thyroid hormone therapy. 3. Blood pressure (BP) \>= 140 millimeter of mercury (mmHg) Systolic and \>= 90 mmHg Diastolic at screening with or without antihypertensive medications. 4. Woman who are lactating or pregnant at screening or baseline. 5. Participants who received any anticancer treatment within 21 days or any investigational agent within 30 days prior to the first dose of study drug. (This does not apply to the use of TSH-suppressive thyroid hormone therapy). 6. Gastrointestinal malabsorption or any other condition that in the opinion of the investigator affected the absorption of Lenvatinib. 7. Participant has history of congestive heart failure with New York Heart Association (NYHA) Classification \> II, unstable angina, myocardial infarction, serious cardiac arrhythmia, or stroke within the past 6 months. 8. Electrocardiogram (ECG) with QT interval (QTc) interval \>= 450 millisecond (msec). (According to Bazett's formula). 9. Bleeding or thrombotic disorders or use of anticoagulants, such as warfarin, or similar agents requiring therapeutic international normalized ration (INR) monitoring. (Treatment with low molecular weight heparin \[LMWH\] will be allowed). 10. Existing anti-cancer therapy-related toxicities of CTCAE version 4.03 grade \>= 2, except alopecia and infertility. 11. Any history of or concomitant medical condition that, in the opinion of the investigator, would compromise participant's ability to safely complete the protocol. 12. Active infection (any infection requiring treatment). 13. Active malignancy (except for differentiated thyroid carcinoma, or definitively treated melanoma in-situ, basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix) within the past 24 months. 14. Epistaxis or active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug. 15. Known intolerance to Lenvatinib (or any of the excipients). 16. Participants with clinically significant laboratory investigations as per the investigator's judgment. 17. Participation in any interventional clinical study within the past 90 days of enrollment to treatment. 18. Male or female of childbearing potential, unwilling to use adequate methods of contraception throughout the study. 19. Participants whom had major surgery within 3 weeks prior to study entry, or who have not recovered from prior major surgery, or whom have surgery scheduled during the course of the study.