After looking around for the plans to a lap desk and only finding them for around $60 I decided I could just as well make something very similar myself. The first one I made had the tray laser cut and then the rest of I made around that tray. After receiving many complements from at work about it I decided that I would design the rest of it as well so you could cut out the entire desk with a laser cutter.
Both the drawer and the box were designed using makercase.com For the outer box I have to work with the pieces a bit because the base is 1/8" plywood and the top and two of the walls are 1/4" with with hinge side using a 1/2" board to allow the screws something deeper to go in it also would allow for a handle to be placed on the Lap Desk

A few notes on the assembly.
The hinges should be recessed on the lids measure the size of your hinges prier to etching them in the lids. I still ended up needing to use a chisel to deepen the slots.
Round the corners on the drawer it will allow it st slide past glue from the corners of the box.
Glue to face of the Drawer last this way you can have the drawer in the box and make sure it is centered on the box and not the drawer.
I was able to find some nice hinges at True Value you get 4 for $2.90 or so for this project you need a total of 6 hinges 4 for the lids and 2 for the leg that folds out of the bottom.