Can cheese be made with lactose-free milk?

Asked by Claydo25 (18) August 24th, 2010 from iPhone

I realize this is probably elementary for most of you, but I haven’t been able to find any documentation about it. Recipes I’ve seen just say “use milk” and stuff, but don’t speak to the science of it. Is the lactose necessary for the process? Will the cheese not form right without it? Can’t you use “lactose- free” milk that still has the lactose, but also the added “Lactaid”?
I read an article that said that that there isn’t really much lactose in a whole mozzarella cheese pizza. It implied that there was more non-countered lactose in Lactaid milk than in a cheese pizza. I find that hard to believe, since every time I’ve tried to just dare my way through 3–4 pieces of pizza, (which I don’t do anymore), it’s hurt me every time, where I can drink near a half gallon of Lactaid milk, (which, by the way, claims to be 100% lactose free), no problem…. Can anyone out there speak to all this? (Also, ditto all this for Ice Cream) ****Thanks****