Looks like the Stan Morantz system,I had or similar . To answer bout lamp shade's.
As per Drapery cleaning; test for sun rot .Your looking for stiff weak fabric.
Remember most are as thin as can be.If so simply refuse.
If not find a suitable vacuum brush tool with horse hair.
You want to vacuum in 4 directions. Be mindful of too strong a vacuum . Keep her gentle.
Up/right side/left side /finish downwards.
A dry cleaning sponge next downwards only overlapping by one inch.
Finish with a dry microfiber.
If you use a dry solvent then apply uniformly and micro fiber down only.
Use a blower or fan on low,if blower further away from the sheer force of the cfm's.
Their cake to do if sturdy.
But if strong don't hesitate ,try friends if you need practice or grab some at good will.
If using solvent always test for colorfastness if more then a single color.In which case replace the solvent with white vinegar misted on first then dried fast.
Color lock the fugitive dye's.
Also blind cleaning with above unit is awesome,diversify if your able !!!
Also clean the inside as well an or vacuum,allow no contaminates to dull your work.
Also Wally Weber was legend,I attended his seminars and have his manual's here. Signed like the rest...