In English this question construction is highly unusual. Perhaps if someone wanted to take their pet lion into a pub, but the barman says, "Only cats are allowed inside", the person might ask, "But, isn't a lion a cat?"
A more usual translated response to this Polish question would be, "Is a lion a cat?"
In Polish it means the same as your pub sentence. Yes, it's not usual, but it's a grammatical structure worth knowing.
The English translation seems technically correct to me but sounds old fashioned and slightly quaint. I agree with adrian's rendering of the English
Would "A lion is not a cat?" be okay, as a reaction not believing what someone else said or is the "czy" indicating, that you have to translate it to a "real" question?