Is metastatic thyroid cancer of the lungs cureable?

Unlikely: Some cancers of thyroid gland retain the capacity to concentrate iodine and may be treatable with radio-iodine. However, spread to the lungs usually indicates advanced disease and many cancers have developed additional damage/mutations and parts of the tumor may not respond and persist.

Most likely not: Thyroid cancer that has spreaded to the lung is unlikely to be curable. However, there are treatments available to control the disease such as radioactive iodine if the cancer cells would pick up iodine. Patient can be treated and maintained with good quality life for many many years with repeat treatment if necessary.