I once experimented (a lot) for my South Bend 34BQ, that has open back gears & non-bath quick change gears. The gears are the end of the headstock are also non-bath.
I had trouble with general chain and rope lubes and with motorcycle chain lubes. They seemed to fly off (on my apron or glasses, of course). Maybe I used cheap stuff?
Some others had objectionable odors for my shop-in-the-home.
One lubricant that I found which didn't fly off & has no big smell was Hy-Per Lube High Performance Oil Supplement Stock Number HPL-201 (hyperlube.com). It's really for putting in your engine (I don't). I got it at a local auto parts chain for about $7.00 a quart to use on an open gear & roller chain project. It worked well there, so i tried it on the South Bend. The manufacturer's propaganda says it has a high film strength and clings well and has no thermal breakdown.
The good side is that it does cling very well. As a matter of fact, it clings so well you can see 'silly strings' of it stretching between the moving gears. Another plus is that, for some reason I can not explain, it does not seem to gather dust quickly. I have a small chip brush that I use to apply it which lives uncovered in the lube tray next to the lathe. The brush does not get dusty quickly.
Another surprise bonus I found was that it quieted the gears tremendously. That's kind of important in my home shop. And, it does not smoke.
The not-so-good side is that if you get on your clothes, it is difficult to remove. From the machine, naphtha takes it off, as does denatured alcohol, but I use medical adhesive remover wipes for wiping it off. (No naphtha odor with those wipes) The lube is 100% petroleum based, so any petroleum based solvent should work to remove it.
It must, after time, let dust cling, but I don't see it. However, my change gears are under the cover of the (open bottom) QC box. The back gears have a guard, but the sides are open. The headstock end gearing is well covered. To be honest, I'm really fussy about my South Bend, so I periodically remove the QC box and clean the gears completely of all lubricants and I wipe down all the other gearing, ways, etc to start over. I suppose if I ignored the lube for a while, dust might be trouble.
I would imagine this is not the ideal lubricant for the job, but it seems to work well for my lathe (and a few other open gear items). Just thought I'd present it for your consideration.
Enjoy Today!
Paul