This is an Expanded Access Program to make lenvatinib available to participants with radioiodine-refractory differentiated thyroid cancer in Brazil. Participants who have no other treatment options available, and who, in the opinion and clinical judgment of the treating physician, would benefit from treatment with lenvatinib will be enrolled. This is a multicenter, open-label program consisting of 2 phases: a 28-day pretreatment phase (including screening) and a treatment phase. Treatment will be provided as long as there is a clinical benefit based on tumor assessments performed according to the center's standard of care and the judgment of the participant's treating physician.

Inclusion Criteria:

• Participants must have histologically or cytologically confirmed diagnosis of one of the following differentiated thyroid cancer subtypes:

  • Papillary thyroid cancer

    • Follicular variant
    • Variants (including but not limited to: tall cell, columnar cell, cribriform-morular, solid, oxyphil, Warthin's-like, trabecular, tumor) with nodular fasciitis-like stroma, Hurthle cell variant of papillary carcinoma, poorly differentiated)

  • Follicular thyroid cancer

    • Hurthle cell
    • Clear cell
    • Insular

• Participants must be radioiodine-refractory or resistant within 12 months of radioiodine therapy and have one of the following:

  • One or more lesions that do not demonstrate iodine uptake on any radioiodine scan
  • One or more 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 posttreatment scanning
  • Cumulative activity of radioiodine of greater than 600 millicurie or 22 gigabecquerels, with the last dose administered at least 6 months prior to program entry

• Participants must have received and failed treatment with sorafenib or have shown intolerance to sorafenib for radioiodine refractory differentiated thyroid cancer.

• Eastern Cooperative Oncology Group performance status of 0 to 2

• Blood pressure less than or equal to 150/90 millimeters of mercury (mmHg) at screening with or without antihypertensive medications and no change in antihypertensive medications within 1 week prior to Cycle 1/Day 1

• Creatinine clearance greater than or equal to 30 milliliters/minute according to the Cockcroft and Gault formula

• Adequate bone marrow function:

  • Absolute neutrophil count greater than or equal to 1.5 × 10^9 per Liter (L)
  • Hemoglobin greater than or equal to 9.0 grams per deciliter (g/dL) (can be corrected by growth factor or transfusion)
  • Platelet count greater than or equal to 100 × 10^9/L

• Adequate liver function:

  • Bilirubin less than or equal to 1.5 × upper limit of normal (ULN) except for unconjugated hyperbilirubinemia or Gilbert's syndrome
  • Alkaline phosphatase (ALP), alanine aminotransferase (ALT), and aspartate aminotransferase (AST) less than or equal to 3 × ULN (less than or equal to 5 × ULN if participant has liver metastases). If ALP is greater than 3 × ULN (in the absence of liver metastases) or greater than 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

• Provide written informed consent

• Males and females, age greater than or equal to 18 years at the time of informed consent

• 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 (eg, 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 program period or for 30 days after lenvatinib 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 program and for 30 days after lenvatinib discontinuation.

Exclusion Criteria:

• Participants having greater than 1+ proteinuria on urine dipstick at screening testing will undergo 24 hours (h) urine collection for quantitative assessment of proteinuria. Participants with urine protein greater than or equal to 1 gram/24 h will be ineligible
• History of congestive heart failure with New York Heart Association Classification greater than II, unstable angina, myocardial infarction, serious cardiac arrhythmia, or stroke within the past 6 months
• Electrocardiogram with QT interval (QTc) greater than or equal to 480 milliseconds
• Existing anticancer therapy-related toxicities of Grade greater than or equal to 2, except alopecia and infertility
• History of intolerance to or progression on prior treatment with lenvatinib that led to the discontinuation of lenvatinib
• Any history of or concomitant medical condition that, in the opinion of the treating physician, would compromise participant's ability to safely complete the protocol
• Females who are pregnant (positive beta human chorionic gonadotropin test) or breastfeeding
• Eligible for any other lenvatinib program that is open for recruitment