I think it's either immoral to ask someone if they have slept with a prostitute, OR it's immoral to lie about it.

It's ok to ask the question if you are a doctor asking about sexual history, or a spouse who is concerned about infidelity. It would be stupid to lie to a doctor (although not immoral), but it would certainly be immoral to lie to your spouse.

I can think of other cases where it's immoral to ask the question. For example, if you're looking for information to blackmail someone. If you think the questioner has malicious intent, then you would lying to avoid damage to your reputation. You have a right to privacy, and lying is the only way to protect your privacy.

There's also a game called "never have I ever", where you would say "never have I ever slept with a prostitute", and then anyone who has slept with a prostitute has to take a sip of their drink. I think this one is entirely subjective. You might be totally open with one small group of friends, and other times you might be playing this with work colleagues.