The lactose intolerant people I knew all do drink de-lactozed milk or non-cow milk. They also eat it with cereals. Practically, somewhat lactose intolerant people eat food with milk inside (whether in sauce or cheese) and avoid only quantities that cause them troubles.

There is really no reason to get offended over that reality. I don't really know why those people consume milk and I was never rude enough to ask. It is their diet. But, they in fact eat it even in situations where they don't have to and go out of their way to get sorts of milk they can consume.