Welcome to Pet Talk! It sounds like your Lily is "kneading" her paws (or what we here on PT call 'making bread')! Is she purring while doing this? If this is what she's doing, it's perfectly natural behavior that starts when they're kittens. Kittens will knead at the mother's tummy to get the milk. No one really understands why they continue to do this other than maybe it's a sign of contentment??

I've also had overweight cats, and that Science Diet really did help! Let us know what happens