The first question you have to resolve is - Was the pen out of round when you finished turning, and before you started sanding on it??
If it WAS round before you started sanding, then a differential in wood removal because of the differences in wood grain is the problem. If this is the problem, you need to concentrate on making a smoother cut while turning so you can sand less and with a finer grit.
If it WAS NOT round before you started sanding, then there was something wrong with your turning, or the mandrel was wobbling.
Turning the wood can make it out of round because of the same grain differences that affected sanding.
If the problem is the lathe and mandrel, it could be anything from tightening bushings too tight against ends that aren't square with the insides of the tubes, to dirt between mating metal surfaces, to a bent mandrel, to misalignment in the lathe or the adapter.
You can isolate the problem further by running the mandrel without wood. If it runs smooth and true by itself, then the cause is something you did after you put the wood on the mandrel; and trimmed ends that aren't square to the tubes is the most likely culprit.