You can actually starve eating only lean meat, even if you an unlimited supply (Rabbit Starvation). That is because you are eating a diet that is almost entirely made of protein, and in order to digest protein, you have to remove and excrete the nitrogen atoms as a waste product (Urea) and your body can't process nitrogen waste fast enough to sustain itself long term eating only protein. Fats and Carbohydrates don't have nitrogen atoms so at least one of the two are needed with the protein to keep you going.