It’s a simple matter to make a holder for a sanding pad so the pad can be mounted on the lathe. The gist of the holder is a disk held by a scroll chuck. The spindle of the sanding pad is inserted into a hole in the disk. The clamping pressure of the chuck jaws locks the pad in place.
One advantage of this arrangement is that you can adjust the RPM of the lathe and thereby control the speed of the sanding disk. Reducing the speed makes the sanding operation less aggressive, and if you use a soft pad, the sanding disk will actually conform to the workpiece to a certain extent. This makes it less likely that you will sand a flat spot on a curved surface.
Mount the blank in your chuck using the tenon formed in the step above. Part off a section of the blank to produce a disk whose thickness, including the tenon, is approximately equal to the length of the spindle of the sanding pad. For the pads I have, this is about 1.25”.
Clean up the exposed face of the disk. Select a drill bit whose diameter is appropriate for the spindle of the sanding pad. My sanding pads have spindles that are nominally 1/4” but are actually a little under size. I find that a 15/64” drill bit gives a better fit than 1/4”. A little too tight is better than too loose. Drill a hole all the way through the disk.
When installing the holder, place the saw kerf in line with a gap between the jaws of the chuck.