I haven't done a CKD in awhile but if I remember correctly carbs, whether it be low GI or high GI, will all knock you out of ketosis. Fructose will do it faster than others due to it's preference to fill liver glycogen. Dextrose is probably the safest carb to eat while in ketosis due to it's preference to fill muscle glyogen stores. However other than these 2 examples I don't think it matters where you get carbs, they will all knock you out of ketosis if you eat enough. Doesn't matter if it's corn flakes or Oatmeal, GI doesn't mean anything as far as ketones are concerned.
And to answer simply, milk is definately not something you want to drink while doing a ketogenic diet. It actually has more carbs than protein, about 13g per cup if I remember right. Lactose is in fact a sugar...