The 2 times I have been caught out with dairy are salt and vinegar crisps, and sliced meats (ham, etc) - not all have lactose in them but some do!
I find the "free from" section is mainly gluten free not dairy! Surprisingly most breads etc are dairy free but have soya in them which lots of milk intolerences are linked with.
We use oat milk with added calcium (the red carton, not orange one) - seems to be only Tesco that do it where we are, so we buy the whole box at once!!! Dietician says they don't normally recommend it as main drink but as Murray never had weight gain issues it was fine. He has Neocate which he used to not like at all, so we pureed fruit with it and made it into ice lollies, then later on made smoothies and yesterday (blender broke!!) tried plain neocate and he LOVED it!!!
If you read the allergy labels they are pretty clear so it doesn't take long to find milk free. We use "Pure" margarine, yellow tub, it is fine for baking too