My DS1 was 9 months old when lactose intolerance was diagnosed and he is 3.6 now, and veggie too. If this is the same thing as your problem then to save you reinventing the wheel, some points you may find useful:
"Pure" dairy free spread
"Lactofree" cheese and milk & yoghurt, in the chillers with other cheese & cartons of milk. Has a big cow in the front. Tastes fine. Milk great to use in porridge, makey it tase creamy for some reason!
"Arla" do a fab vanilla desert in little pots of four. Usually in the free from range in sainsburys - tastes just like custard & is great cold or warmued up in to microwave
We had SMA LF (lactose free) available on demand on prescriptionfor DS1, free as it was for him. We used it until about a year ago when we realised you could buy lactofree, which tastes nicer. We still have a couple of tins in, just incase we run out of lactofree. has your doctor prescribed it for your DS2? We would get it six or eight tins at a time
oh and " Swedish Glace" vegan ice cream is fab, as are "Dairy free" 'chocolate' buttons (oh I know,...but all main stream chocolate is off limits so he gets hardly any treats)
Seems to tolerate a couple of jaffa cakes nowadays - hardly any choc on, and dark at that so very occasionally he has one or two as a treat.
Eating out was a bit of a pain,(for a long long time he would not eat potato either..aagghh!) I agree, though I hve always made a point of telling staff I have brought his food and everywhere I go I have never encountered any problem/refusal of entry etc.
Finally, just wanted to thank the posters for rallying to to cause. I always take something new from this sort of thread. And to say to you that once you become product savvy it all becomes second nature after a while. (Checking labels, would be amazed at how much stuff has milk or cheese init!) At 3.6 DS1 knows why he cannot have certain things and perhaps importantly, why and he really has never taken issue with not having certain things.
Good luck, it gets to be ok after a little learning curve