Actually, most people are intolerant of lactose in milk. It is a true allergy, but also a sign of how our milk is processed. People who are lactose intolerant usually do better on whole milk or they do sell a brand called Lactaid. Be very careful with soy milk alternatives, as sometimes they still contain soy. You will need to be very viligant reading the label. Most commonly used is almond or rice milk. However, if you really want to make sure you are getting pure almond milk, cashew milk, etc make it from scratch at home! If you google something like "homemade cashew milk" or "cashew milk recipe" you will find a good bundle of info.
Actually we just went soy free, and gluten free to help deal with some health issues I have.
So other things you have to look for are items like soy lechitin, soy oil, etc. You have to learn all the components that soy beans are derived into so you can read labels more easily. In my opinion if you don't understand the label, then you shouldn't probably be consuming it anyway.
You are welcome to PM me, and I can give you more info you want. We have already replaced a lot of our food with the soy-free versions, and there are a few books that might help you as well.