Yeah, that's what I thought, too, that there wouldn't be the need for a snap ring if it were held on elsewhere. My trepidation comes from the fact that it is a 40+ year old lathe, and coming across parts for it (or rather, that don't cost kind of a lot) is getting harder with each day that passes - and messing up a spindle seems like the kind of thing someone should really avoid if at all possible.There should be a key so the pulley can drive the spindle. I would expect that grunge is preventing the pulley from slipping off. Keep working at it with WD40 or kerosene to loosen the grunge. Try rotating the pulley back and forth to work the solvent into the bore. If it were mine, I would try a gear puller with gentle force. Pull a little on the gear and douse with solvent and tap pack with a soft face hammer or block of wood and a hammer. Repeat this operation multiple times. You will see more and more movement with each iteration and finally, it will pop off.
Edit: if there were another retention mechanism, they wouldn't have used the snap ring.
I'll gather answers for a bit longer before actually taking action here, but to my inexperienced eye, this does seem like the best idea so far. Thanks!