It differs from dog to dog. So far I've yet to run into lactose intolerance with mine, but as Wolf suggests there is a high incidence of it in puppy dogs. The milk fat can also cause some GI problems.

My previous dog expected a small bowl of carnation instant milk every morning. My current oldest puppy doesn't think much of it, while I suspect the younger one would gobble it up. So powdered milk is another option.