Milk is not very high in carbs, but perceptually it is quite high, and therefore, not a good idea. There are exceptions though, say you lift heavy weights 3–6 times per week. To consume 1 liter of milk directly afterwards will be very anabolic, and although lactose is not perfectly suited for turning into muscle glycogen, 50 % of the carbs in the milk are. Remember that carbs that enters your muscles as glycogen, does not “count” when you’re staying within keto-levels. It would be a good idea to consume milk, as the protein is the best you can get, and milk itself is anabolic (it’s created to make a calf grow into a full grown cow/ox.), without considering the protein.