Regular dairy cheese has natural animal fat. If it's made from milk that has fat in it. Now, if the milk used to make the cheese is lowfat or fat free then the cheese will be low fat or fat free. If it's made from soymilk or rice milk it will probably not have animal fat in it, but will have whatever fat content the milk has in it, or whatever fat content (which is probably vegetable fat hopefully) that has been added to stablize the veggie cheese.
I am lacto ovo, and I am because I love cheese!