I probably am mildly lactose intolerant because milk and its close associates, yoghourt and cream make me feel sick, and, as a result, anything that tastes of milk has the same effec.
However, I do not like milkless tea. As a result I use skimmed UHT milk, for the simple reason that it is totally devoid of taste or smell, but still has the 'softening' effect of milk in tea and the like.
My daughter is at the other extreme she loves milk, preferably green top straight from the farm. I cannot even touch the bottle, because of the aroma, my stomach has an instant reaction.