My cat Toby has the same food obsession that started when I brought Havoc home (even though it was 3 days later and they knew each other beforehand). I feed them obth at the same time but Havoc is easily distracted so I fave to follow him around with the food bowl until he finishes, or lock it in the pantry closet to keep Toby from eating it. I have to put the kitchen trash in there too or Toby will get into it. He'll also jump on the counters and pre-rinse any dirty dishes we haven't put in the dishwasher yet. Sounds like the same kind of situation with your cats. I think Lucy sees Baby as competition for food, even though she's not to the point of outright aggression. I assume they get along, even if it means they ignore each other? My guys have never been best pals, but the only time they really really fight is if Havoc smells another cat, but only sees Toby. Toby is the dominant one so he doesn't take kindly to threats from Havoc. All Hell breaks loose after that, and I have the scars to prove it.

Like Freedom said, I'd get Lucy checked by a vet just to be sure that her obsession is purely behavioral and not a nutritional deficiancy. Also, to see if a possible dental problem makes her want to chew. If it's behavioral then there are a few de-stressing products out there to try. A medical deficiency can be corrected with a diet change or supplement.

Some cats just don't gain weight as easily as others do so if Lucy isn't overweight then she may just have a high metabolism or otherwise be burning off calories. My Toby would weigh 20 pounds and eat me out of house and home if I let him, so I really have to work at keeping extra food out of reach.