Well, while we're waiting on more skilled help, here's some things to ponder.
First, it's really not rocket science, but little details are a big deal.
Make sure you have a way to adjust the lathe. Do you have leveling feet on it already? Make sure they're loose and easy to adjust.
The level needs to sit at a good place, and sit there correctly. Best to find a surface that isn't worn and is representative of the ways. The little pad the tailstock sits on works well, not sure if it's big enough or not. Then you need to sit it traversely. Might need a couple accurate gage blocks or parallels to hold the level above the vees and be indicated off the level pads for the carriage and tailstock. Doubtful the top of the vees is a good location.
Also, make sure the bottom of the level, and where it's going to sit, is nice and flat. Debur the area with a fine stone or something.
So then, just go about leveling. It's a back and forth procedure. Level it long ways, then across.... lather rinse repeat. Make small adjustments with the feet, and wait for the bubble to settle out.
Oh, make sure the level is calibrated, it should read the same no matter the orientation. Flip it end for end to verify.
These levels can be accurate enough to show movement based on where you stand, so I'd stand in the same location for each measurement, otherwise you'll chase your tail around and around.
Hope this helps a little. Just give it a shot, nice thing is that you can't really mess anything up. Be sure and check it again in a couple days, see if things have settled out. Check the lathe traversely along the ways, look for twist in them. You'll likely be able to take that out with proper leveling.
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