John -- there were two issues in your original message -- the answer to one - do you need another lathe -- that answer is yes, of course you need another lathe. Every turner should have more lathes. That answer is independent of tuning up your current lathe.
The measurement and adjustment is a function of a lot of variables. Clean is one of them. The object is for the alignment of the center of the headstock spindle to be continued through the tailstock centerline. Lathes sold in the US are european designs that control from the face of the center of the ways laterally, and the surface of the ways vertically. The sloppiest (least control and most "slop") are those with a couple of steel tubes that the tail stock slides on, and the best are machined ductile iron.
This is a tradeoff now between how much error is there vs how much effort to reduce it -- and the accumulation of crud, sawdust, bed corrosion, chips, ect all contribute to accretion of errors. How you measure is important because a sloppy fit of tooling into the head stock and tailstock measure as alignment errors that are attributable to technique and tooling rather than the lathe. Many think that a drill chuck that they get for 30 buck is somthing more that a sloppy fit and runouts exceed 0.05 on one of mine. A good chuck costs up to 10 time more to reduce the error. (note that is 50 thousands almost a 1/16th of an inch)
I have to start with a damn good cleaning to eliminate the crud, chips - especially in tapers and in the ways and tailstock. Cleaning and inspection of tooling ( amazing what dropping a MT onto concrete will do for adding runout at the spindle - and that little burr gets magnified).
So tell us more about what you have -- remember that paint and lipstick on a pig still leave you with a pig.