By the time we have "one-million-person cities" on the moon, synthesizing water or hauling it from icy asteroids will not be a problem.
(Paraphrasing a bit but I do remember reading such an article, where they explained how it was nonsense to send interplanetary messages with their long wave omnidirectional antennas and inefficient early radios, including the immense amounts of coal that would have to be burned to run the steam machines powering the dynamos. In the end we had a solar powered lander sending images back from Mars in 1997, using a couple wats.)
On the Moon, this is what may be lacking.
On Earth, we can close loop recycle from drains. We can take sea water and desalinate. We can use osmosis and clean dirty ground water.
Is any of that cheap? Nope. But it's also not a blocker on having water to drink and bath with.
We will never run out of water, only "easy clean water".
Not that it matters to your point about the moon.