Inclusion Criteria:  Age ≥ 18 years at the time of informed consent Histologically or cytologically confirmed DTC (including papillary, follicular or Hürthle Cell carcinoma) Progressive (biochemical or anatomic) disease for which lenvatinib is started as standard treatment at the discretion of the treating physician Measurable disease at baseline imaging (F-18 FDG PET) according to the definition of the Positron Emission Tomography Response Criteria in Solid Tumors (PERCIST) 1.0 with at least one lesion ≥1.0 cm in the longest diameter for a non-lymph node or ≥1.5 cm in the short axis for a lymph node.  RAI-R disease on structural imaging, defined as any one of the following:  Metastatic lesions that are not RAI-avid on a diagnostic or intra-therapeutic RAI scanperformed prior to enrolment in the current study RAI-avid metastatic lesions which remained stable in size or progressed according to RECIST 1.1 criteria despite RAI treatment. Absence of response is observed during 6-9 months after high dose I-131 therapy.  No recent treatment for thyroid cancer:  No prior I-131 therapy is allowed <6 months prior to initiation of therapy on this protocol (a diagnostic study using <400 MBq of I-131 is not considered 131I therapy) No external beam radiation therapy is allowed <4 weeks prior to initiation of therapy on this protocol. (Previous treatment with radiation for any indication is allowed if the investigator judges that the previous radiation does not significantly compromise patient safety on this protocol) Eastern Cooperative Oncology Group (ECOG) performance status ≤2 (or Karnofsky ≥60%) Life expectancy ≥3 months Ability to swallow and retain orally-administered medication and no clinically significant gastrointestinal abnormalities that may alter absorption Creatinine ≤1.5 mg/dL (≤133 µmol/L) or estimated glomerular filtration rate (eGFR) (using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula) ≥50 mL/min/1.73m2 or 24-hour urine creatinine clearance ≥50 mL/min/1.73m2 Adequate blood coagulation function as evidenced by an international normalized ratio (INR) ≤1.5  Adequate bone marrow function with:  Absolute neutrophil count ≥1.5*10^9 /L Hemoglobin ≥9 g/dL (5.6 mmol/L) Platelets ≥100*10^9 /L  Adequate liver function with  Albumin ≥25 g/L Total bilirubin <1.5x institutional upper limit of normal (ULN) with an exception for patients with Gilbert's syndrome Aspartate aminotransferase and alanine aminotransferase ≤3x institutional ULN (≤5x ULN if subject has liver metastases) Negative pregnancy test within 7 days prior to starting the study for premenopausal women. Women can be included without pregnancy test if they are either surgically sterile or have been postmenopausal for ≥1 year. Sexually active women of childbearing potential must agree to use a highly effective method of contraception during the study and for at least 6 months after the last study treatment administration.Sexually active males patients must agree to use condom during the study and for at least 6 months after the last study treatment administration. Also, it is recommended their women of childbearing potential partner use a highly effective method of contraception. Effective methods of contraception are defined as those, which result in a low failure rate (i.e., less than 1% per year) when used consistently and correctly (for example implants, injectables, combined oral contraception or intrauterine devices). At the discretion of the investigator, acceptable methods of contraception may include total abstinence in cases where the lifestyle of the patient ensures compliance. (Periodic abstinence [e.g., calendar, ovulation, symptothermal, postovulation methods] and withdrawal are not acceptable methods of contraception.) Voluntary agreement to provide written informed consent and the willingness and ability to comply with all aspects of the protocol  Exclusion Criteria:  Concomitant or previous malignancies within the last 3 years. Patients are eligible for this study if they have been disease-free of the previous malignancy for at least 3 years, have a history of completely resected non-melanoma skin cancer and/or have indolent secondary malignancies. Symptomatic or untreated leptomeningeal or brain metastases or spinal cord compression  Evidence of cardiovascular risk including any of the following:  Clinically relevant arrhythmias Acute coronary syndromes, severe/unstable angina Symptomatic congestive heart failure Use of other investigational drugs within 28 days preceding the first dose of treatment in this study or during the study Have a known immediate or delayed hypersensitivity reaction or idiosyncrasy to drugs chemically related to lenvatinib and/or to Thyrotropin alfa (human recombinant thyrotropin) or other known contents of the two drugs. Inability to follow a low iodine diet or requiring medication with high content in iodide (e.g. amiodarone) Patients who received iodinated intravenous contrast as part of a radiographic procedure within 6-8 weeks of study registration. Patients are eligible for this study if urinary iodine analysis reveals that the excess iodine has been adequately cleared after the last intravenous contrast administration Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection or psychiatric illness/social situations that would limit compliance with study requirements. Pregnant, lactating or breast feeding women Any medical or other condition that in the opinion of the investigator(s) would preclude the participation in a clinical study Unwillingness or inability to comply with study and follow-up procedures