Problem with lead screw/half nut/s

[Hawkeye]

The leadscrew deflection could mean that the half-nuts aren't lined up properly with the screw. I don't know how you would check/fix that, but it may be worth looking into.

Sometimes you can lessen chatter by slowing the spindle speed. Easier on a lathe with variable motor speed - you can do it on the fly. If the workpiece is long and thin, chatter is almost a foregone conclusion, without a follower rest.

All the advice in the previous posts are right on the money - sharp tools, on centre, proper speeds and feeds.