If my mom's stage 3b lung cancer is responding well to radiation therapy, is it likely that she will recover completely?

It depends: The overall 5-year survival rate with stage 3a lung cancer is 23%, but it can vary widely. The 5-year survival rate with stage 3b lung cancer is sadly only about 10%.

Possibly.: The answer is in the statistics. There is a 15 to 20 percent chance of cure with radiation and chemotherapy. 10 percent with just radiation for stage iiib (3b). Therefore how do you define likely? Even if not cured she can actually recover? (from pain or breathing problems or bleeding) and do well for months to years but then not recover when the cancer comes back.

Interesting?: Usually stage iiib means a T4 tumor or nodes on the other side of the mediastinum or low neck. Most get chemotherapy together with or followed by radiotherapy. Patients getting that treatment have roughly 1 chance in 3 of doing well for a long time. For radiotherapy alone that chance is remarkably less. Group statistics never tell what happens to a single person.