2. Find Me in Your Memory - ML has hyperthymesia (almost perfect recall of own life - so a brain and I guess a mental health issue) and has been seeing a psychologist/psychiatrist (cannot remember) since he was a kid. (The actor was also in Coffee Prince)
3. Her Private Life - ML, cannot remember what the technical term for what he has. (This actor was also in Coffee Prince - didn't realize when I remembered this title).
I know quite a few dramas where the leads should be getting help :)
Bonus: The Bride of Habaek - FL is a psychologist (kinda lousy one though, lol) so doesn't quite count.