The primary purpose of this study is to compare the progression-free survival (PFS) of participants with radioiodine (131 I)-refractory differentiated thyroid cancer (DTC) and radiographic evidence of disease progression within the prior 12 months treated with lenvatinib 24 mg by continuous once daily (QD) oral dosing versus placebo.

This study will be conducted in 3 phases: a Prerandomization Phase, a Randomization Phase, and an Extension Phase. The Extension Phase will consist of the Optional Open Label (OOL) Lenvatinib Treatment Period and the Follow-up Period.

Inclusion criteria:

1. Participants must have histologically or cytologically confirmed diagnosis of one of the following Differentiated Thyroid Cancer (DTC) subtypes:

   a. Papillary thyroid cancer (PTC) i. Follicular variant ii. Variants (including but not limited to tall cell, columnar cell, cribriform-morular, solid, oxyphil, Warthin's-like, trabecular, tumor with nodular fasciitis-like stroma, Hürthle cell variant of papillary carcinoma, poorly differentiated) b. Follicular thyroid cancer (FTC) i. Hürthle cell ii. Clear cell iii. Insular

2. Measurable disease meeting the following criteria and confirmed by central radiographic review:

   1. At least 1 lesion of ≥ 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 Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 using computerized tomography/magnetic resonance imaging (CT/MRI). If there is only one target lesion and it is a non-lymph node, it should have a longest diameter of ≥ 1.5 cm.
   2. Lesions that have had external beam radiotherapy (EBRT) or locoregional therapies such as radiofrequency (RF) ablation must show evidence of progressive disease (substantial size increase of ≥ 20%) to be deemed a target lesion.

3. Participants must show evidence of disease progression comparing (a) scan in screening and (b) historical scan obtained within 12 months prior to signing informed consent, according to RECIST 1.1 assessed and confirmed by central radiographic review of CT and/or MRI scans.

4. Participants must not be eligible for possible curative surgery and must be radioiodine (131 I)- refractory / resistant as defined by at least one of the following:

   1. One or more measurable lesions that do not demonstrate iodine uptake on any radioiodine scan
   2. One or more measurable lesions that has progressed by RECIST 1.1 within 12 months of 131 I therapy, despite demonstration of radioiodine avidity at the time of that treatment by pre- or post-treatment scanning.
   3. Cumulative activity of 131 I of > 600 millicurie (mCi) or 22 gigabecquerels (GBq), with the last dose administered at least 6 months prior to study entry

5. Participants may have received 0 or 1 prior vascular endothelial growth factor/ vascular endothelial growth factor receptor (VEGF/VEGFR)-targeted therapy (for example sorafenib, sunitinib, pazopanib, etc.). Each of the VEGF/VEGFR targeted agents will be counted individually, regardless of the duration of its administration.

6. Participants 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 one month.

7. Participants must be receiving thyroxine suppression therapy and thyroid stimulating hormone (TSH) should be ≤ 0.1 milliunits/Liter (mU/L) (≤ 0.5 mU/L if there is safety concern).

8. All chemotherapy or radiation related toxicities must have resolved to < Grade 2 severity per Common Terminology Criteria for Adverse Events (CTCAE v 4.0), except alopecia and infertility.

9. Participants must have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 - 2.

10. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤ 150/90 millimeter of mercury (mm Hg) at screening and no change in antihypertensive medications within 1 week prior to Cycle 1/Day 1

11. Adequate renal function defined as calculated creatinine clearance

    ≥ 30 mL/min per the Cockcroft and Gault formula

12. Adequate bone marrow function:

    1. Absolute neutrophil count (ANC) ≥ 1500 per cubic meter (mm3) (≥ 1.5 × 10^3/micro liter [μL])
    2. Platelets ≥ 100,000/mm3 (≥ 100 × 10^9/ liter [L])
    3. Hemoglobin ≥ 9.0 gram per deciliter (g/dL)

13. Adequate blood coagulation function as evidenced by an International Normalized Ratio (INR) ≤ 1.5

14. Adequate liver function:

    1. Bilirubin ≤ 1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome
    2. Alkaline phosphatase, alanine aminotransferase (ALT), and aspartate aminotransferase (AST) ≤ 3 × ULN (≤ 5 × ULN if participant has liver metastases).

15. Males or females age ≥ 18 years at the time of informed consent

16. Females must not be lactating or pregnant at Screening or Baseline (as documented by a negative human chorionic gonadotropin [hCG] test with a minimum sensitivity of 25 international unit per liter (IU/L) or equivalent units of 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.

17. 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 (ie, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing).

18. Females of childbearing potential must not have had unprotected sexual intercourse within 30 days prior to 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 participant 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 prior to dosing and must continue to use the same contraceptive during the study and for 30 days after study drug discontinuation.

19. Male participants must have had a successful vasectomy (confirmed azoospermia) or they and their female partners must meet the criteria above (ie, not of childbearing potential or practicing highly effective contraception throughout the study period and for 30 days after study drug discontinuation). Those with partners using hormonal contraceptives must also be using an additional approved method of contraception, as described previously.

20. Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol

Exclusion criteria:

1. Anaplastic or medullary carcinoma of the thyroid
2. Two or more prior VEGF/VEGFR-targeted therapies or any ongoing treatment for 131 I-refractory DTC other than TSH-suppressive thyroid hormone therapy
3. Prior treatment with lenvatinib
4. Participants who have received any anticancer treatment (including Chinese herbal medicine specified for the treatment of tumor) 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.
5. Major surgery within 3 weeks prior to the first dose of study drug
6. Participants having > 1 + proteinuria on urine dipstick testing (Participants with urine protein < 1 g/24 hour (h) will be eligible).
7. Gastrointestinal malabsorption or any other condition that in the opinion of the investigator might affect the absorption of lenvatinib
8. Significant cardiovascular impairment: history of (a) congestive heart failure greater than New York Heart association (NYHA) Class II, (b) unstable angina, (c) myocardial infarction, (d) stroke, or (e) cardiac arrhythmia associated with impairment within 6 months of the first dose of study drug
9. Prolongation of corrected Q wave and T wave (QTc) interval to > 480 millisecond (ms)
10. Bleeding or thrombotic disorders (Treatment with low molecular weight heparin [LMWH] is allowed.)
11. Radiographic evidence of major blood vessel invasion/infiltration
12. Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug
13. Active infection (any infection requiring systemic treatment)
14. Active malignancy (except for DTC or definitively treated basal or squamous cell carcinoma of the skin, or carcinoma in-situ of the cervix or bladder) within the past 24 months
15. Known intolerance to any of the study drugs (or any of the excipients)
16. Any medical or other condition which, in the opinion of the investigator, would preclude participation in a clinical trial
17. Females who are pregnant or breastfeeding