Milk is mostly water.
That business of "have 8 glasses of water a day" comes from some bloke in the 1940s, and his study also mentioned that most people get most of that water from their food. Bread is half water, for example. And anyway more recent research shows it's a useless generalisation, depends on climate, individual body type, physical activity, a zillion things.
If you want to drink 4lt/day milk, I advise building it up slowly. At the fastest, begin with 1lt/day in the first week, 2lt/day in the second, and so on. Your guts have certain bugs and enzymes in them that help you digest. Eat more of one food, get more of those bugs, eat less get less.
That's why if a vegetarian eats a big pork roast one day they get the squirts - their guts don't have the bugs to do it anymore, they should have begun with a small piece and built up over time if they wanted to eat meat again.
Most people if they jumped straight into drinking 4lt/day milk would get the squirts or really farty. Build up to it.