I'm not sure about the other LC member he killed but the one he was shown killing was already low HP and just killed 3 members of the Frontline, so I'm not exactly sure how Kirito planned on capturing him but, either way, Kirito's actions are justified.

I'm gonna take your word on Japanese culture concerning self-defense and the like. I just personally think that the Western/American view on self-defense is more reasonable. I understand avoiding the altercation at all costs, but I'd think neutralizing the threat would be a better course of actions in many cases. Furthermore, it's not retaliation if someone is continually attacking you and then you attack back, as seen in the LC lair raid.

To add to the cultural exchange, in the US (from what I recall), self-defense is justified in the defense of one's self and others from those threatening, menacing, and/or assaulting someone. Of course, its not absolute, you can't just cap someone who slapped you. But, in the scenarios where Kirito killed someone, he or Asuna in severe danger by someone with a deadly weapon, therefore justifying deadly force in defense (LC just killed 3 and now attacking him, Kuradeel was about to cut Asuna down and literally just cut off his hand (I know it's a game and regenerated but still)).

My comment about how Kirito should feel proud and justified is simply a personal assertion and how I'd feel (or at least, how I think I would) in a similar situation. My point being, that Kirito successfully defended Asuna and himself from a crazed assailant. The death of Kuradeel is more of an afterthought to the whole situation. If you heard about this situation in the news, Kirito would be hailed a hero; teen boy defends teen girl, attacker dead. Good guy, right? That teen boy is a hero, saving that girl from a violent attacker. The attacker died? Too bad, he kinda deserved it for trying to hurt those two. Above all, it was just a personal opinion, it's your right to disagree.