OK, let me get this straight...she found your dog, admitted to seeing the posters, but decided to keep her anyway. Then she gave you money for her, which you now have in your possession.
I really don't understand the decision you made in the first place to allow her to keep the dog. She was wrong in the first place to keep her, knowing she belonged to someone else. It doesn't matter how attached she got to her, Lucy was not her dog to keep, and she thought she could just buy her from you. You should have called the police at that point rather than letting her essentially buy the dog from you. However, you accepted the money rather than telling her no, and demanding the dog back. I guess now it is a question for the police, or an attorney if it comes down to it. It depends on how much you actually want Lucy back, or you have chosen to let her go and let these other people be her owners now. But if Lucy is upset and stressed out because she is in a home that is not hers, that is at least partially your fault for choosing to take the girl's money and basically letting her keep her. It's not fair to have an animal that loves you unconditionally, be it's owner all it's life, and then put a price tag on that. If you really want Lucy back, then talk to her and see if she is willing to give her back if you return the money, but I also have to wonder how much money it actually was if you think it's enough to help with car repairs and medical treatment. I'm sorry, but this whole post is very odd to me and just doesn't make a lot of sense - but maybe because the actions you took in the first place, accepting money for a dog that you claim to love and miss dearly, don't seem consistent with someone that would do anything to get their dog back. Don't make this about how "people with money" feel entitled to whatever they want if they just pay enough - you still accepted it instead of standing your ground and going to the police in the first place.