Coming from someone who has quite a few mental illnesses, I thought I'd reply to this topic with my standpoint. IRL, I suffer from depression, ADHD and panic disorder, all of which have been diagnosed.
Now, with LOTC being as chaotic as it is, I strongly believe that there should be some form of mental illness implemented in roleplay. When your character is faced with stressful situations, whether it be the death of a friend or being attacked by another, you can't expect your character to be completely "fine." Of course, there may be some characters that are completely devoid of emotion, but that occurrence is rare. Each of the core races on LOTC have emotions and it's our job as roleplayers to express those emotions as we rp.
Scientifically speaking, stress builds up overtime. As our cortisol levels rise, it can have negative impacts on our brains and development. For example, if your character is faced with numerous stressful situations, they might end up developing some sort of anxiety, or even depression, etc. Lastly, I believe that, before you get into mental illness rp, you should be well informed and educated on the mental illness you are planning to roleplay. I know I'm practically rewording what others have said in the replies before mine, but I'm restating what they've said because I truly agree. By being educated, you can easily avoid roleplaying out anything that may come across as offensive to those who suffer with mental illnesses IRL. In my opinion, if you are planning on roleplaying out a mental illness with the goal of gaining attention from doing so, don't bother roleplaying a mental illness at all. IRL, mental illnesses are things we cannot control, and although I do not speak for everyone who has one, I'm sure we all wish we didn't have any in the first place. Just think about that before trying to seek out attention through this type of rp.
