I'm Italian, and completely lactose intolerant (since four years).
We don't drink it after 11pm because cappuccino is essentially a breakfast drink and that's all.
Asking for it in some places at the wrong time automatically define you as a foreigner and/or maybe a weird customer.
Asking for a caffè macchiato is a different story, you can have it whenever you want, and it's quite common.
If you're lactose intolerant ask for soy (more available) or almond milk (less available) for your cappuccino/macchiato, they are available almost everywhere.