"Dyrene kan lide mad" is just as accurate. Just as "Kan du lide ham?" (Do you like him?) is just as accurate as "Kan du godt lide ham?". The "godt" is an adverb that gets added to the sentences to make them more unambiguous, as in clear. Where with "Kan du godt lide ham?" it also makes it more 'personal' along with unambiguous. If you like, you can take a look at the Wikipedia article to get some more info on adverbs.
I am very confused about the above statements about "lide" meaning suffer...yes in a different context. Don't we also have English words that have several meanings for one? Eg, bear can mean the animal or it can mean to take on a load of emotional strain. Just because it can also mean suffer does'nt mean that is actually whats being said here. Its all in context.