Should i give my ring back to my boyfriend. My friend say he's lying about it?

It's the thought that counts. If he spent the time wandering around a parking lot, looking for a ring, then he obviously cares at least a tiny bit. Or it could be his mother's. Have you asked his mother? That would be a smart thing to do. Don't put out (especially if you don't want to) just because he "found" you a ring. Just check your facts before you throw all of his romantic intentions away.