Instead of forcing the lean cat to eat in a "prison", like a carrier box or a closed room, you could take advantage of the fact that the fat cat is just that; fat. Can he jump as high up as the lean one? Can he fit through a hole so tiny that the lean cat is just able to wiggle through?
Find such place in your home that only the lean cat can jump onto, and put the food bowl up there. Show the place to the lean cat, so it'll know where to find food. The fat cat can't get there; problem solved.
Example of a cat's ability to jump and climb:
(This animated gif is found in several pages in internet, I don't know whom to credit for it.)
I currently have this situation with our cats. We have five cats, the youngest of which is overweight. I feed four of the cats on kitchen counter. This one cat is not willing to jump even this much, a relatively low (85 cm/34 inches) height for a cat, but simply waits on the floor until I give him the leftovers after the other cats have all eaten.