Poor Lily. I agree with Jenny. Try cleaning it if you can take a flashlight and have someone hold her while you inspect the paw more.. in between her toes really good.. on the pad, around the pad etc.
I wish Peanut would wear shoes on our walks! So many dangerous things on the ground! We were on a walk and I didn’t realize there was glass everywhere.. I noticed as we were stepping in it . I immediately picked him up, sat down on the curb and looked at his paws. One of which were bleeding. We got home and I made DH hold him while I looked with a flashlight. There was no glass stuck, a piece just cut him. Very small cut, but I still cleaned him up.. I also wish people were more careful with what they are throwing out on the ground..
Hopefully Lily’s paw gets to feeling better!! I would definitely take a second look, because if there is something in there you will need to pull it out!