In theory, I mean, and hang the expense. To start with, is one-sixth g enough gravity to hold an atmosphere?
As I understand it, yes it can be terraformed in theory. The gravity IS enough to hold an atmosphere for about 100,000 years as I recall. Supposedly you could keep the atmosphere essentially permanently by using orbital shrouds, which would be just thick enough to bounce stray atmospheric atoms back.
What are “orbital shrouds”?
Orbiting membranes, rather like a solar sail; very, very large, and very, very thin. They’d orbit the Moon, and intercept enough of the slowly drifting away atmospheric atoms to keep the atmosphere from dissipating.
Wouldn’t cosmic debris shred this membrane? The lunar surface is a veritable ball of swiss cheese.
You said hang the expense so you would go mine the asteroid belt for large ice chunks to use for water and oxygen of course.
I’m not sure how you make enough fertile soil but if you’re patient build a large magnetic accelerator catapult (as per Heinlein) and ship animal waste and wet trash up in large quantities for a long time.
In the long run you have the problem of no magnetic field to deflect charged particles from the Sun, radiation levels would be rather high, specially during a solar flare. On the plus side it could put evolution of Selenite species into high gear… 
The moon is not terrafomable.
It is however, lunaformable.
I would say the moon is already lunaform.
Not true. To terraform is to make a planet/moon terra-like. It literally means Earth-Shaping but the point is to make it like Earth.
To lunaform would be to make a planet/moon luna-like.
I’d consider a breathable liquid atmosphere rather than a gaseous one. Think that’d work?
point conceded
The first thing we need to do is guide a comet into the moon at just the right angle that will give it some spin, say one revolution every 24 Earth hours. That would bring a bit of gas as well. That idea is from pulp sci-fi somewhere, I don’t know who thought of it first. The time scale for something like this would be thousands of years per stage, and each stage would only make the moon very slightly more earth like.
You’d have to set up meteor defenses, and repair the damage from all the tiny stuff that slips through.
We can make breathable liquids, but I don’t think the Moon could hold onto it any easier than it can to air; there’d be surface evaporation.
We’d probably do something like that for the water, but it would probably be faster and easier to set up an orbiting system of mirrors if we need to compensate for Luna’s rotation.
A lot of that is from the high-impact early solar system, though.
The rate at which the moon is being struck now is orders of magnitude lower than the rate at which it was struck in the earlier, formative years of the solar system.
Edit: Sorry, MrDibble, didn’t see your post.
That of course depletes the Earth of biomass.
Trash and poop? Heavens, no!
Sounds carbon-friendly to me.
You do understand how the ecosystem works right? Trash and poop is filet mignon to some species.
I understand we have more of these two things than the Earth would have without us.