Timelooping Stories

Lux Arc wasn't really the best protagonist you could ever ask for. He was a normal dude. A bit of a sarcastic ass and prone to a smidgen of cynic views, but no particular traits worth mentioning. It didn't help how a hyperactive time traveler girl who just happened to come crashing in his life managed to make him more jumpy than he already was. What's her game to all of this?