anna doesn't really know lucy that well, but she's impressed that lucy managed to walk away from a weird random encounter in bosuma without being too messed up by the process. it's a sign of the right kind of mindset to handle the real deep dives that this place is gonna demand of them in the very, very near future, or at least the ones that anna anticipates taking part in.

she also heard about how freya protected lucy down there, and that helped improve her opinion of lucy a bunch, too. she trusts frey, and if lucy is someone that frey's apparently close enough to to protect like that, she's gotta be good people, right? that's what anna thinks, at least.