I lie about having a cat all the time.
Why do you choose to lie about your cat?
I don't tell people about my cat because I think they are allergic to cats.
Some lies are not that bad, however some lies are really bad and can make people lose their trust on you. You could lose their friendship if people can't trust you.
I'm trying to look cool by hiding my cat.
I am not sure that makes you look cool and you can harm people if you lie and they are allergic. You'd be better off finding a new home for the cat if you think you don't want a cat.