We must start with Lucas's mother, trite as that may sound. Evidence derived from Myrna's blog and Facebook suggest she excessively praised her "beautiful boy." He's heard he is Mommy's handsome baby his entire life. This is understood to be an overreaction to Lucas's lack of popularity and general social ineptitude as a child. He didn't get affirmation, attention or praise from anyone else, so mommy buried him in it.
Thus, Lucas enters life thinking he's attractive, because mommy says so. It's one of his core beliefs.
There are other factors to consider, and I'll struggle for brevity. First, we should address Lucas's very highly developed sense of self esteem. He is willing to believe anything positive about himself and ignore all evidence to the contrary. If a desperate hambeast in 2007 said he waw cute, he will remember it forever. If someone once said "You're tall," to Lucas this is unassailable proof of how hot he is.
Note that Lucas also shifts definitions and standards to suit him. Broke? Fine, socialism, doesn't matter. Someone uglier got a bae? Fine, that just shows he's plenty good. Fat? No, used to be deathfat, etc.
Lucas is also, in a sense, frozen in time. He is stuck in highschool, still chasing the type of girls that rejected him. He doesn't understand how he's aged.
Moreover, Lucas is, as we all know, delusional. Who knows how he reads his reflection?
Finally, Lucas lacks self awareness, and the ability/desire to see himself through other's eyes. This makes him even more resistant to the terrible realization he is a wretched oaf.