Setting up a lathe is not high tech. You must be careful, keep everything spotlessly clean and make multiple measurements with every step. Regrinding the bed of a lathe rarely produces increased accuracy, but what it does do is allow tight carraige adjustments which reduces chatter and adds overall machine stiffness. This increases consistancy making every step more repeatable. A worn out, loose lathe is capable of accuracy, but takes a lot of patience and experience to do that. When you service a lathe bed, every surface on the bed should be remachined to original specs. Any attempt to do otherwise is a waste of money. For those folks that have never done this, let me assure you that lathe beds look massive and enormously stiff, but they are not. They can and do bend and twist quite easily. That is why the bed leveling operation is so critical. Please do not misunderstand that statement, a level lathe is NOT important. They are quite successfully installed on ships. What is important, is bed straightness and reference to a water level is nothing more that a common base line reference. All lathe beds will twist with the weight of the carraige simply sliding across them. A lathe carraige is not balanced. It is much heavier on the apron side and when moved to the center between bed supports, will exert a twist as much as .004" worst case. Contrary to popular opinion, this will not cause an observable change to the dimensions of the cut because the position change of the tool rotates about the bed center. This is the reason a worn bed does not cause inaccuracy.
Head alignment does effect the lathe's accuracy. It is critical, so getting the spindle line parallel to the lathe bed is the second step in setting up a lathe. That is why a precision test bar is so important, because it easily shows these position errors. Every spindle comes with a precisionly ground inside cone. Typically it is a morse taper and the test bar seats there and provides a spindle extension on which a simple dial indicator is placed. The top of the bar has a ground flat which is positioned during testing, parallel to the bed. Observed deviation is vertical head misalignment. When the indicator is positioned 90 degrees away at the horizontal center any deviation along the bar's length indicates horizontal deviation. This deviation can be compensated with shims under the headstock.
These statements are verifyable with two tools, a precision machine level and a test bar and if you don't have access to them, get access or buy them. These are necessary to install a lathe, let alone repair one. Steve