Gregory
Welcome to GJ, and you asked a very good question, I am learning my self but what I have seen I can share with you. Some vises have the lead screw underneath the jaws that are not hidden, I have seen these lead screws with a C clip or even a snap ring that pulls the moveable jaw back, adding shims or a spacer would tighten the backlash. Remember the Lead screw pulls the moveable jaw and the clip returns it.
The Wilton Barrel vises use a horseshoe washer that fits into a groove cut into the lead screw, see my picture, the groove is cut into softer steel than the washer so most of the backlash comes from the wear in the groove. No grease is the culprit here.
The older vises like the Starretts and have a acme nut located in the back of the square slider in a dove tail angled channel that is pinned in loosely, some times the pin gets wore, bent and the acme nut block slides forward and backwards till it stops, you can really see this by just pulling and pushing the moveable jaw.
Then another cause is either the square or acme threaded lead screw is just plain wore out, and this also could be the nut. When this happens replacement parts are needed.
Tear into your vises is the best way to fix your vises, please share your pictures before you sell them, we all enjoy looking at old or new vises.
I am interested what other members have to say because I am just getting into these vises my self.