I'm highly skeptical of it paying for itself. Even if we knew that the moon had an abundance of every single element needed for manufacturing, it would still be an effort unlike mankind has ever seen to build a self contained base there. It has been discussed in the past how manufacturing on earth relies on a whole chain which has taken hundreds of years to develop. Absolutely everything would need to be shipped up there from earth, operating a mining base would be enormously expensive, I don't think you'd ever recoup even a small fraction of that. All of the Apollo missions combined wouldn't even come close to a drop in the bucket of the amount of stuff we'd need to haul to the moon.
If you are thinking off the same discussion that I can remember, that was with regard to setting up a mars colony, which I agree seems too hard to be feasible in the foreseeable future.
Sending material from the earth to the moon is cheap in comparison to sending material to mars though, and there is potential to make it much cheaper in the future (that requires more infrastructure in orbit, which in turn would be cheaper to create once there was factories on the moon). Sending material back from the moon to earth is basically free.
A moon colony wouldn't be nearly as isolated from earth as a mars colony. Travelling back and forth takes a few days and there is only a few seconds communications delay. It would provide lots of benefits to earth which would mean there would be a mutual interest in keeping things going.
You wouldn't have to send
everything up there from earth. It would probably begin with a research base, then you would begin to set up small factories that can produce bulk materials, like water, oxygen, aluminium, titanium and silicon. Bulk material for buildings can be constructed with the help of lunar soil for example. The low gravity environment helps when building large structures. Once you get the ball rolling, it will only be very specialised and difficult to make parts that needs to be shipped from Earth.
The raw materials you can mine on the moon (and eventually from nearby asteroids) would last for a very long time. The surface area of the moon is almost the same size as eurasia and it can all be mined.
The Apollo program took place between 1960–1972 and technology has improved enormously since then. Even so, it will no doubt be very expensive to get the ball rolling, but once the basic infrastructure is in place it will provide an almost infinite supply of the raw materials which we are quickly running out of here on earth.
Realistically, if we started today it might not break even in our lifetime, but I do think it would pay for itself eventually (if successful).