At best Lelouch has some mild sociopathic tendencies with mild psychological problems. And at worst he's a self-aware psychopath with extreme sociopathic tendencies and with zero morals when it comes to achieving his goals.
He considers those he's close to as his 'possessions' and things 'that belong to him' which is why he saw absolutely no problem thinking about setting up Suzaku and Nunnally so that they could both be happy before Suzaku became Euphie's knight, but he cares for his 'possessions' deeply even if it would be detrimental to his health and his plans.
He also has no qualms about considering his allies 'his pieces on a chessboard' although that could also be his way of coping with being the leader of the Black Knights. If he considered all the soldiers he'd lose for every operation he'd never be able to plan effectively so considering them his pieces was probably one of the only things keeping him as sane as he was for a lot of the first season.
After his enemies start taking advantage of his connection to his 'possessions' in the second season, that's when he starts to lose it and begins to do anything he could think of to keep them safe even if it would ruin his plans and his reputation. It's also why betrayal of those he's close to hurts him so much, because his feelings toward his 'possessions' are a very strong sense of love, though not necessarily romantic in nature, and it hurts him greatly to have them not feel the same level of dedication that he does for them.
Still think he was one of the single best characters ever created though.
I've always considered him having very minor mental problems, they wouldn't be an issue besides maybe a bit to possessive normally or even non-existent. However when you add in trauma, living with a family that numbers in the likely hundreds and more than 99% of them hate you because of your mother and your father ignores you at best. Than his mother dies, his sister is crippled and he's shipped off to another part of the world to live. Than he's made to walk through a destroyed land filled with bodies, carrying his sister(shown in one of his flashbacks). This isn't even counting the whole being in charge of a rebellion against a world super power with limited resources. And who's his version of a therapist? C.C. a sarcastic immortal. He can't even go to anyone else ie wanted to because no one else knows everything. Or at least that's how I've always seen him, as having less mental problems and more just heavily traumatized which is why he's so cold and possessive.
Well, I suppose that is one way of looking at it, but if you look up Sociopath on TV Tropes there are a bunch of eerie similarities between Lelouch and the Tropes that make up The Sociopath. That's sort of why I drew the conclusions above.
I never said it made him bad, in fact he has officially become one of my most favorite characters of all time. Right up there with Kiritsugu from Fate/Zero. The two of them both fought for peace no matter what they had to become and they did all they could to accomplish their goals.
he reminds me a little of the Count of Monte Cristo... sorta, gains power and uses it along with masterful plans to exact revenge, but struggles when the consequences are not those he'd expected...(i'm talking about the actual book not any movies with that title horrible things never go near this point). Lelouch reminds me of him a lot actually...