Not even mentioning the enormous boon to nanomaterials, metallurgical, and other such research. Certain materials and components have already been established as much easier to make in low gravity. Engineers are pretty much guaranteed to come up with more.
Can I try to hold you back from such a red-herring?
There are processes that are easier to deal with in zero (or near-as-makes-no-difference-zero) gravity conditions, and there are actually a lot of things that (through past expertise at least) we find gravity useful for.
Lunar industries are subjected to gravity big enough to make a lot of the former advantages go away and not big enough to
necessarily allow a full shift of equipment from Earth to Moon.
For examples, you can separate items of different densities by a fractional column, on Earth, and a simple centrifuge in space. (In space, the fractional column wouldn't separate, and while centrifuges are used on Earth they're usually mounted axis up/down and gravity is actually part of the "take from the centre, take from the edge" removal method, but is intentionally neutral insofar as how far from the axis the particles flow.)
Also glass-making in space (or similar extrusions to flat planes) might be doable, but the method of creating flat glass on Earth (floating over a bed of molten tin, IIRC) might not work quite so well on the moon if the liquid doesn't flatten so quickly...
Not that there aren't things that would work in 1/6th Earth normal, and
some maybe a bit better (the kind of manufacturing process that needs supportive components to prevent the piece-in-formation bowing under gravity could be done on the moon with less supports... handy if the supports create weak-points/deformities in the finished piece), but space factories are probably the 'big catch' for most of the exotic manufacturing processes. Moon-base industries, I foresee, will mostly be supplying the building moon-surface infrastructure, with a second line in building components from the raw materials that will eventually form the structures of space-going vessels. (Rather than hoist the unrefined ores to space from the Moon or doing the initial fabrication at the bottom of Earth's gravity-well.) And this latter industry may well be usurped by asteroid sources, when we're reached out that far...
There are some things (the vacuum of space, perhaps near enough total 'for government work') that are
almost attainable on the moon, so maybe a combo of "need gravity, need vacuum" industry could be best done there. Better than trying to make gravity (
sans significant Coriolis forces) in space or vacuum (to the best ability of our air-pump technology to extract the significant proportion of free-floating gas, in vessels of sufficient size and also strong enough to withstand the forces, and dealing with the introduction/extraction of materials if it's intended to be a continuous process) down here on Earth. For those, I say: The Moon Is Where It's At! (Probably!)