I made a wooden jig in which I drill three small holes to insert the brass wires for soldering to the lamp ring.
A small brass disc center the ring during soft soldering.
Some of the lamp components.
"Glass" disks are cutted out from an old floppy disk box.
To turn the plastic disks without damaging them I have thought about pressing them between two short brass rods, one in the three jaw chuck and the other in the tailstock center.
Some picture of the finished lamp. The glass burner tube is a turned and polished from a plexiglas scrap.