We could start with "Do at least 1/3 of the population think it's justified?" I believe that puts depression on the "no" side and painful terminal illness on the "yes" side with extremely large margins. Work from there to refine the criteria.

That is indeed a difficult question. I doubt a perfect answer is possible. Existing suicide-assisting organizations e.g. in Switzerland typically rely on individual assessments based on extended dialogue with the person wishing assistance and their doctor.