Why does lactose intolerance (mild case) cause stomach pain?

Gas production: From what i remember of biochemistry, lactose intolerance is your body not breaking open the sugar molecule lactose. That leaves all of the sugar to be eaten by the bacteria that line your gut to eat it. They produce and you feel the gas byproduct. If you have a slight case of lactose intolerance then you can partially digest the lactose. Lactaid does a great job of breaking up that sugar.

Lower bowel: It should not cause stomach pain but it does cause lower bowel pain. If the lactose has not been broken down and absorbed in the small intestine due to absence of lactase, the lactose then becomes available for the bacteria in the lower bowel to ferment leading to production of gas and liquid leading to distention of the bowel and thus the pain , gas, and loose bm.