As far as I really know anything about this: the answer could be yes, no or to both. You could react to milk, you could react to lactose or to both. If you have MC and do the Enterolab testing, the outcome can be that milk (dairy) is one of your intolerances and causes MC. In that case the reaction on milk is a reaction of your immune system to casein (same as with soy and gluten). If lactose is the problem, your bowel can not digest the lactose, due to a lack of an enzyme in the small bowel. It enters than the colon undigested, what can cause problems as diarrhea, cramping, pain and gas. It is quite simple to find out if lactose causes your problems, just try some lactose free dairy and see how you react to it.
But both reactions can be related. Lactose intolerance can have different causes. Sometimes it is genetic, quite a high proportion of the world population can not digest lactose. Other causes can be a bowel disease, like celiac disease but also Crohn and MC. Due to the bowel disease, lactose is not digested anymore. If the bowel disease is cured, digesting of lactose should than not be a problem anymore.
So theoretically the casein in milk could be the course of MC which also results in lactose intolerance.
the stuff you are asking about (if I understand it well), is drops that you can add to the milk to break down the lactose (what normally the small bowel would do). What I have read about it, breaks it only down up to 90% of the lactose. So quite a portion is left. If you buy lactose free dairy product, there is only 1% or 0,1% left. Some cheeses are lactose free. Hard cheeses should be lactose free, soft cheeses are not. For the Dutch hard cheeses I know for sure that they are lactose free (at least the bovine ones). Brands of other countries I have no idea (no chauvinistic reasons

) I know all this stuff because I have been lactose free for about two years before I was diagnosed with MC.