Dawno's Do It Yourself Portable Beading "Lap Desk"
I've taken a wide shoebox lid and fit an 8"x8" bead mat inside of it. By the way, bead mats are just a square of vellux material - you could probably find it at a fabric store and cut your own - in my googling I found a cute one at Etsy with edging, a sewn in tape measure and tie strings at the ends so the whole thing could be rolled up - probably not a good idea to try it with beads still inside, though *grin*.
Where there's space left over in the box top, I've put some small plastic containers and the spool of stringing wire. I used the box top, initially, to sort the lighter colored faceted roundel beads from the darker ones, and darker pinched oval beads from the lighter ones, so my finished lanyard necklace would be uniform in color - thus the tiny spoon lying there, which I used to help sort and set aside the unneeded beads.
The bead mat keeps the beads from rolling all over the place and makes it easy to pick them up on the wire since they stay pretty well put, the plastic holders keep the smaller spacers from finding their way under the mat. Since the box top is just 8" x 12", it fits very nicely on the lap.
By the way, here's the finished necklace lanyard, tentatively named "Chateau Picard"