Can radiation therapy cure a stage 4 adenocarcinoma in the lung?

Probably not. Most stage 4 have many sites of spread and can not be cured by radiation. However there are a few cases of limited stage 4 such as a single metastasis to the brain or liver in which a low percentage of patients could be cured.
No. Stage 4 adenocarcinoma of the lung is not curable. Radiation can be used to treat some of the symptoms related to the cancer.
Probably Not. Most of the time radiation is given to stage IV patients to either increase their longevitiy (usually measured in months) or decrease pain symptoms (ie from metastases to bone or chest wall) or 3) for poorly controlled bleeding from the tumor. Radiation typically does not offer a cure for stage IV patients.