I also have lactose intolerance, but it is not based on fat content. With lactose intolerance it is the sugar in diary (lactose) that your body cannot digest. When your body lacks the appropriate enzymes (lactase) to digest the lactose your system will (in my experience) try to dump/expel it as fast as possible. Coincidently when you have diarrhea you also expel all of your lactase enzymes. So after having an overdose of lactose and diarrhea you will loose what tolerance you may have built up. You can build up your tolerance (usually) by avoiding dairy as much as possible so your body can heal and stock up on enzymes. This would allow you to eat small regular amounts of diary while maintaining a healthy digestive system.
Fermented products are easier on your system since there are bacteria already in the product breaking down the lactose for you. Harder cheeses are also easier to digest than softer. I can have butter, cheese, yogurt, and the occasional ice cream. However a cream sauce, brie, or glass of milk would push me over the edge and I would have to avoid it completely for a while. So many people tell me they've gone to Dr. after Dr. for diarrhea and no one told them to avoid dairy. (I worked at a health food store)
Fermented products are easier on your system since there are bacteria already in the product breaking down the lactose for you. Harder cheeses are also easier to digest than softer. I can have butter, cheese, yogurt, and the occasional ice cream. However a cream sauce, brie, or glass of milk would push me over the edge and I would have to avoid it completely for a while. So many people tell me they've gone to Dr. after Dr. for diarrhea and no one told them to avoid dairy. (I worked at a health food store)