Thanks for all of the great input! My trimmer came out and she did not square the hooves but trimmed as much as she felt comfortable with and we agreed that we'd have her trimmed more often and see if that helps. I think I like that solution as well.
I do think that Lily is just being lazy - when she is feeling good she has no problem picking up her feet.
On another note: I just bought some Renegade hoof boots for her and my trimmer put them on and Lily completely freaked out at first! She started stomping, jumping and lunging forward and I thought for sure that she was going to fall down in the aisle! I took her off the lead rope and let her run around in the paddock on her own and boy was she prancing!! It took about 3 or 4 minutes for her to just calm down and mellow out. Then of course she inspected every inch of those "things" on her hooves. After that she was like "what boots?" - what a stinker!!
Again, thanks for all the help!