Make a decision on your desired diameter target and work out your segment size to suit.
I use my version of
Segment Calculator to do this.
The next operation is to prepare your basic stock and if you use my cutting method of using a Chop Saw, make sure stock is square on all faces.
The narrow pieces can be cut from a thin strip but I more often just slice them on the chop saw.
Check the segment length, and note that you just flip the stock 180 to cut a new segment.
As long as the Chop Saw is set up square and angles are correct then there is no need for sanding of segments, indeed I find the resultant joint lines are better given off saw finish rather than a fine sanded finish.
Clamp the segments firmly, I use jubilee clips, if the angles are correct then there is no need for messing about assembling 180 deg sections and sanding them to fit.
The top and bottom,
The bottom is roughly prepared to form a socket for future turning of assembled parts and then reversed to prepare the mating surface to match the cleaned up segment ring, likewise the top mating surface prepared.
It is essential that all mating surfaces are flat across the faces, use a steel rule and check for 'squeaky' sound when slowing lathe down, once heard it becomes an easy and quick way to prove flatness.
Glue and Clamp the three parts, you only need to rough turn the outers, just size within reasonable dimensions so that it is easier to align the pieces.
Then all that remains is to mount the rough assemblies on the chuck and clean up the outer, part out the central top waste and form the lid opening and clean up the inside.
Meanwhile a few spare lid blanks get their turn in the jubilee clips.