It is held in place by gravity and a pair of magnets — I glued one on the back of the lid, and one into the printed monitor mounting arm. The extra weight somewhat limits the angle of the laptop screen: if I recline it too far back, it goes flat. But it's totally usable on a table.
The screen runs from USB power, and takes only 1-2 W. I had to modify the preregulator inside so it's stable from 5 V.
I can share the SCAD files if anyone's interested; the monitor has a standard 75-mm VESA mount.