So I get why Archer is obsessed with Lancer, but if you’re willing, could you go more in depth into why Lancer finds Archer interesting?
archer's very existence challenges the premises that lancer builds his identity as a hero on. lancer has always conceived of a hero as someone who is memorable, who shines brighter than the other stars if only for a moment, but archer is a complete nobody who doesn't even want to call himself a hero. the fact that someone like archer can keep up with him forces lancer to reconsider what makes him a hero too. clearly it's not fame or pride, because archer has neither but is his match all the same.
it really pisses lancer off that archer takes no pride in himself, because archer is good. archer is skillful as hell to be able to keep up with the legendary cu chulainn. lancer's initial hostility towards archer was about archer not taking him seriously, using disposable swords to fight him instead of the bow that should be his noble phantasm as an archer, but by their second fight in ubw it's become about how lancer can't stand to see someone this obviously capable deny his own worth like this. if he managed to become a heroic spirit surely he has succeeded at something in his life? surely there is something he can take pride in and fight for as a hero?
archer denies the very notion that a hero's life is worth taking pride in and lancer's response is to try to vaporise him with the noble phantasm that embodies his own heroic pride, but while lancer is overwhelmingly the victor of that clash he didn't actually defeat archer. lancer isn't wrong, a hero cannot be perfectly good and save everyone because the world simply isn't that black and white, and to be a hero therefore is to be memorable and take pride in what you have achieved. but archer isn't wrong either, if all it takes for a hero is to be memorable then even the vilest deeds devoid of pride or honor can be washed away with conveniently heroic results.
neither can deny the way the other challenges the premises of their heroic ideal, and so being around each other forces them to conceive of themselves as people outside that heroic ideal. that's why they became so close seemingly overnight in fha and why they keep running into each other across time and space. their sense of identity, the concept of a hero that they attempt to live up to, has shifted to incorporate the other's views.
