Yes, soy milk is a good alternative, rice milk can be your choice as well.You can also have vegan cheese which is also lactose free, but i wouldn't advice you to eat goat milk unless you are not lactose intolerant but one of the 1-in-10 people who is allergic to alpha S1 casein protein, the protein you find in cow's milk and has the same symptoms when consumed.Both goat milk and human milk lack this protein.Nevertheless, many people that are lactose intolerant and consume goat milk have no problems, for reasons not well understood; they think it's because the goat milk does not leave residue in the colon for fermentation, which causes the symptoms of lactose intolerance.
Bottom line, you won't know unless you try, simple as that. But soy milk is the best alternative by far.