I don't know much about lathes, but if you are indicating runout on a piece of drill rod in the chuck, the runout is probably in the chuck itself. If that's not the case, the spindle nose may have an internal taper that a 5C collet would fit into and you could indicate off that or even the internal surface of the nose itself, particularly if it's a large bore spindle. At any rate, be sure you're checking the spindle, not a piece in a chuck. If the chuck is off the lathe, there may also be some place on the outside of the spindle nose to indicate on. Drill rod may not be perfectly round, but if you are indicating a piece in a 4 jaw chuck and can't adjust the runout to less than .0005" you probably do have radial spindle runout or worse yet, axial. I don't know what to tell you except it should have precision tapered roller bearings with locking adjusting collars that can take any slack out of the bearings. If that doesn't work????????
Hopefully, someone who actually knows what they're talking about will jump in.
In my very limited experience, if you're reading off the spindle itself, there shouldn't be any runout. Even a "last word" should hold still.
Good luck, Tom