It is an oddity of English that many nouns which are normally count nouns may also be used as mass nouns when talking about them as foodstuff. Example are chicken, egg, cake, pizza. (Unfortunately this does not apply to all foodstuffs, and I don't know any way to predict reliably which it does apply to. You can say I like cake/cakes or I like pizza/pizzas, but I like pancake or I like muffin sound very odd to me).
In the case of an animal, such as lamb, if we use it as a count noun, eg "I like lambs" we always mean those things jumping around in fields, whereas "I like lamb" unambiguously refers eating lamb-meat. (As others have pointed out, for some common animals, we have different words for the meat. If you say I want some cow, people will think that you must mean beef, but think you're deliberately using an odd word for it).
If we use animal names as mass nouns, it is almost always taken as food, even if they're not something we normally think of eating. So, for your example I like cat means eating the meat from cats. Similarly, I can (truthfully) say "My father was once given bear", meaning that he was served a dish of bear-meat.