In order to digest lactose, humans produce an enzyme called lactase. However, some people have an inability to digest lactose and are diagnosed with lactose intolerance. There is a difference between being lactose intolerant and having dairy allergies. Typically, dairy allergies are an allergic reaction to the proteins found in dairy products.
Goat's milk is thought to have slightly less lactose then milk from cows. However, whether or not the amount of lactose is low enough to make goat's milk easier to digest for people with lactose intolerance is debatable. Regarding dairy allergies, if a person is allergic to the milk proteins in cow's milk it is likely they will be allergic to goat's milk as well.
It's important to note, however, that many types of cheese are naturally low in lactose whether they're made with goat, cow or sheep's milk. Most of the lactose is found in the whey, which is the moisture that is drained out of cheese to make solid curds. As cheese ages, it loses even more whey. The longer a cheese has been aged, the less lactose will remain in the final product.
There is another reason that goat's milk might be easier to digest that has nothing to do with lactose. Goat's milk is naturally homogenized, meaning the fat globules are small and remain suspended in the milk rather than separating out. This makes the milk easier to digest. In cow's milk, the fat globules are large enough that they can be hard to digest.