One way to do it, costs some money, would be to make or preferably purchase a ground Morse taper 3 alignment bar with about 12¡± of straight length. I have such a bar that I purchased from an eBay seller a few years back. I also have a MT2 alignment bare which is useful for checking the tailstock and will work on a 6¡± Atlas lathe spindle. Clean the spindle taper, install the bar in the spindle, and use a dial indicator and mag base on the carriage to check both vertical and horizontal alignment running the dial indicator back and forth on the top and front or rear face of the alignment bar.
Perhaps you could achieve the same check if you had a nice new three jaw chuck installed on the spindle and used a nice straight length of 3/4 or 1¡± diameter drill rod instead of the alignment bar in the spindle taper.
I have several pdf¡¯s on lathe alignment and various methods of checking lathe alignment and condition if you think those would be useful to you let me know and I will send them to you via email.
Steve Haskell
Troy, MI
Steven H