My mom has a lactose free milk (cow milk), which is good, my cat likes it too ^^ (my cat is old but never grew out of her milk addiction). For yogurts, she eats those made with ewe or goat milk (beware of the fat though). Soy milk or yogurts are fine, but not exclusively. As for cheese, the refining process is said to kill lactose, so a little won't harm you.
For cooking, we use soy cream, her milk, or rice milk, and coconut milk for certain recipes. The only real issue is whipped cream, all the plant based alternatives don't have enough fat or thickness to make a good whipped cream.
Eating gluten free is relatively simple if you cook yourself (there are other cereals), not that i ate a lot before but even for the occasional laziness all the ready meals at the supermarket are to be avoided because if you're a celiac, even possible crossed contamination is too much. I'm not a celiac, however gluten makes me bloat, and i have trouble with barley and rye, they cause wreak havoc in my intestines. guess what flours are used in traditional gingerbreads
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The only trouble i have is baking gluten free. I always cut my flour with corn starch for fluffy cakes, but i can't find a good replacement for wheat flour. Some specialised brands make special blends of flour, but they're pricey and not easily found.