Helpfull hints for beginners or how to suck eggs for most of you experienced machinists.
The process is mostly only called levelling because a level is used in the process and it is very occasionally helpfull if it is level though that is mostly on milling machines. It is really "untwisting" the bed. A tilt is ok but it needs to be a consistent tilt. Therefore the level does not need to be calibrated, just repeatable which you can check by lifting and replacing it in the same place a dozen times and observing the variation in result. Then set the bed with the same tilt at each end and if that is also dead level then fine but don't sweat over it. If your lathe bed has Vs or other non flat shapes place parallels or eg tool bits on a flat bit to produce a higher reference points.
Rather than taking cuts use a new bar that you have checked for straightness by rolling on a surface plate or milling table, and checked for roundness at the measuring points only with a micrometer.
Mount it in the 3 jaw fairly straight . Mount a dial indicator for horizontal reading at center height.on the saddle or if on cross/top slide pull up all slack and lock them. Rotate the chuck to find the peak reading and mark position with felt pen. Record reading, rotate 180 and read again. It doesn't matter that the chuck/bar is not true – the difference in the readings tells you where the center is. You can cross check by testing at 90 & 270.
Return to mark, run saddle along to far end of bar, take reading, rotate 180, and again the difference tells you where the center is. I don't think it actually matters if the bar is a bannana or your second set of readings is taken at a different rotation of the chuck. The key is you have found the center each time without taking cuts.
You obviously assume the saddle travells down the bed with a consistent relationship to the center line (though not true if it is worn, or long and stressed into a camel). The two centers measured above are the true line of the mandrel in its hopefully true tight bearings so should be the same unless the head is scewed. Costs nothing to adjust and repeat.
When you have got the horizontal sorted repeat on the vertical line using the indicator above the bar.
The tailstock alignment also does not need a cutting operation. Set up a bar between centers and measure where the centerline is in the same way provided your drilled centers are true. If not you can turn just the ends but bot the body which will relieve stresses and create a banana.
A better way is to take the trouble to drill the centers on a better lathe or set up on the steady so you have an unmachined bar with true centers that can be used for setting the topslide inline.