As a Lactose Intolerant person I almost always get diarrhea when I drink milk.
But even if my stomach spits it out the other way, is it atleast able to extract the protein from it to build muscle? If so, how much?
If you're getting diarrhea, your ability to absorb any nutrients from what you've eaten is severely compromised. Anything you've eaten hours earlier that isn't finished digesting will also leave you with suboptimal nutrient absorption. The irritation to your intestines will also decrease your ability to absorb nutrients from subsequent meals for some time. It's not worth drinking any milk if you're lactose intolerant.
Just get whey protein, that's where most of the protein in milk is anyway. Alternately you could try yogurt, as the fermentation makes it palatable for some people. Also, goat and sheep milk can also be palatable for some people who can't drink cow milk.