It costs about $100K per kilo to "lob" something into orbit, let alone sending it to the Moon.
That will be cut significantly by the space elevator. If that fails then a really big slingshot will obviously be the solution.
It's better to use ice that's already in orbit. Which, coincidentally, there is plenty, along with methane and other useful compounds.
We just need to go and get it. The first group to successfully accomplish that will signal the true dawn of the space age.
Is the $100K per kilo based on rocket technology? I'd be very interested in other delivery mechanisms that would be too harsh for humans or electronic equipment, but would work fine on ice or liquid water. I remember the Canadian who was working on Saddam's Supergun originally started his work on using artillery to shoot things into orbit. Since the massive acceleration from such a gun would not be an issue for simple, raw materials, what do you suppose the cost per kilogram would be?
Find a passing comet full of ice and redirect it to hit the moon (try not to hit the earth while you're doing that).
So get out to the outer system and lob huge chunk of ice from Saturn back to the moon.
It's only 100K to send from Earth because the USA lacks the will to use better systems.