Amber would've probably told her off a few times about what prefecture is all about and how Lily should be proud to be one. If Lily did her duties well and hid all shennanigans away from Amber then Amber wouldn't have a problem with her. She respects all prefects by default.
Dom and Lily were on the Quidditch team together! I think that they would've had many many after practice chats and stuff. Close cousins, then? :)