He really should do something about Livia, no matter how much he claims he wants to keep himself apart from her and pretty much everyone else, despite still insisting on attending the school and even saying aloud the only purpose of the school is to find spouses. Leon is so full of contradictions. In fact I think the dude is suffering from some degree of mental illness, like mild schizophrenia. He says he couldn't stomach killing a human, yet he was exceedingly brutal, psychologically and physically, during the simple match where he represented Angelica against Marie's harem. Of course it wouldn't have made even any sense to kill anyone in those fights, but you could say he went as far as possible in insults and actions. All in all he should have gone through considerable trouble as an adventurer, even if the manga made it look like a very short escapade. Someone with a flimsy attitude shouldn't be capable of that.
Also at the end of this chapter you can see he's very naturally intimidating and doesn't give a single shit about the local noble's troubles, nor anything else. How does that fit togeter with a person who supposedly couldn't handle killing a clear enemy in a fight?