You are not measuring spindle runout with that setup. You are measuring chuck body runout, which is well within reason, and has no effect at all on your parts. To measure spindle runout, you have to remove the chuck, and measure the spindle nose.
Lifting the lathe by the spindle is not a bad thing, more than adequate strength in that area, at least on smaller lathes. I normally lift by put a strap through the hole in the bed then use a 2x4 as a cross piece.