Why....
The mentally ill part is the most important aspect for someone actually being a lunatic. By your loose interpretation, everyone in dragon age is a lunatic.
Actually, yea that sounds about right, lol. In fact, Solas seems more sane than the majority of people we've met.
The guy think he alone can save the elves, but he doesnt like the new elves, he want to bring back the ones who are long dead.
He is ready to make extreme measures to accomplish his objectives, be it giving his orb to a Darkspawn magister (who would think its a good idea) or killing someone he consider a friend to ursurper her power.
He is delusional, he is ready to kill a lot of innocent people and I think he is suffering from a trauma, from awekening mind find his actions led the elves to their destruction.
Still I dont hate him, that just my interpretation of him. You can disagree with me if you want, Im not trying to convince you.