I had to go lactose free within the first few weeks of coeliac diagnosis and, despite numerous attempts to gradually re-introduce it to my diet, I am still just as, if not more so, intolerant to it.
I find it very easy at home - as the other posts have said there is tons of stuff either lactose free or made from goats milk or soya. Personally I am also intolerant to soya but this isn't a big deal.
When I'm out and about it can be a nuisance so I always carry the milk portions with me. It is now a matter of habit to have milk and GF cookies on me at all times!
The milk portions are a godsend - they are not fresh so you will find them in the long life milk section. They are normally on the shelf in a large box with the front pulled off so you can see them inside. I always check the date, which is printed on each portion rather than the bar code label so you have to check it through the net bag but they are normally good for several weeks. I can get them in all my local supermarkets. This is what they look like:-