Found out the problem, and its fairly unbelievable. Nothing to do with UV, or smoothing or displacement settings:  if you lathe a polyline, once the  vertex object is finished, then before you leave the modeller you MUST delete the polyline which is still sitting on the working box.  After that the vertex object will take displacement shaders with no problem at all.

Not sure if there is a reason for this, or if it is a bug.  Thanks to all who suggested fixes.