If the cat is not your cat I dont see it being an issue!!

I loved the name Lily but growing we had a dog called Lily and I know that my parents and brothers would associate name with dog first as it was when we were VERY young.

A friends DH has name of 1 of our dogs, she thought it was funny when we told her dogs name and to be honest I did not even think abou it when I sugessted name to DH for dog.

If you love name go for it as you will not have the cat in family forever and it is not your cat ITMS.