I've never been diagnosed for lactose intolerance but milk does mess me up too, gas, diarrhea, etc.
I used ON Gold Standard WPI with water, which does contain some lactase. I'm not a doctor but lactase is different from lactose and I'm not sure it would cause a reaction since lactase breaks down lactose. I never got diarrhea or anything from it. You might want to try out a small package of it before buying a huge tub though.
I want to try shakes with milk so I think I'm gonna try lactaid and see if it makes the shakes taste better.
Also, someone here posted about
Digestive Advantage which seems to be a daily supplement that helps with lactose intolerance. They said Rippetoe suggested it, so maybe you want to look into that. I've never taken it though so I can't give any info on it besides that.