In Brazilian Portuguese it is most common to say "estar com fome" (be with hunger), which is the fully written out form of the sentence you wrote (Eu tô com fome = Eu estou com fome).
In this case, Brazilians would probably say "O leão está com fome or informally O leão tá com fome. I hope it helps!
Not much, here are the literal translations:
Eu estou com fome -- I am with hunger
Eu tô com fome -- "tô" is a simplified version of "estou", used in speech but not accepted as a translation, just like "wanna" wouldn't be accepted for "want to". Very common in speech.
Eu tenho fome -- I have hunger (not as common, but not incorrect)
Eu sinto fome -- I feel hunger (also not as common, but not incorrect)
As you can see, the first is the most used in writing, the second is the most used in speech. The last two are alternative ways of saying it, but they are not as common. =]