We used masking tape for painting walls to cover the areas that should stay lighter. Using an x-acto knive and a cuting matt with a ruler prooved to be helpfull to have a variation in the strips. Cut some wide, some small, some long, some short. Alternate to create the pattern, the death star wasn't all the same, neither should be yours.
We created a stencil of the round weapon on a piece of paper first and traced that onto the Lamp with a pencil.
I'm adding the scanned template of the laser in 3 versions. We did it by hand so it was a bit hard to scan that, but maybe somebody can use this as a template. It fits on a sheet of A4 paper and is meant for the 52 cm diameter version - for the smaller ones you'll need to size it down a bit.
This step took a good bit of patience but it's worth to take your time and go wild on details.