Kathy, I agree with curt on this one, the pulleys are most likely not moving freely to allow the speed to change smoothly and to change at all. The belts or belt can wear out but you would still have some speed changes and at certain points when the pulleys are at their smallest is where you would possibly see slipping but not real loose or sloppy belts. So if you are going to go through and clean everything you may as well put new belts on too. The shined up pulley surfaces really have little to do with things and the smooth surface makes better contact with the belts so scuffing them up will just wear on the belts and potentially wear the pulley out sooner.
Dry graphite powder works well for a lubricant and does not attract dust like oils and grease. Just keep it blown out with air every few days and you should be OK.
New lathe is best fix, good luck,
Jeff
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