I usually just stick the sleeve/desk (sans strap) in my backpack, but you could use it on its own with a strap as shown.
Step 1: What You Need
I cut a piece of 1/8" thick laminate pressboard I had lying around a little smaller than the dimensions of the bag and then filed and sanded the corners and edges smooth. You could use any material that is light and stiff enough.
And then some 1" wide stick-on velcro that was lying around.
Disclaimer: I know it is a bad idea to heat up plywood, because it will give off toxic gasses, but I have no idea if this would be a problem for the amount of heat that a laptop might generate. Always compute in a well ventilated space!
Step 2: Put Velcro on the Bag
When you do this, stick a thick book inside the bag to help you press down on the velcro to get a good seal on the adhesive. Also use your fingers to press from the inside and outside to make sure they're really stuck on there good.
I thought about sewing the velcro on, but it was nearly impossible with the thick padding of the sleeve, and the adhesive seemed to be plenty strong for this purpose.
Step 3: Put Velcro Onto the Wood
When you are happy with how they are positioned, peel off the backing and then press the piece of wood down onto the velcro.
Have a book inside the bag/sleeve like before so you can press down nice and hard to get a good seal. When the hook velcro is on the wood pretty good, carefully separate the wood from the bag and press on the velcro with your fingers some more to make sure they are well attached.
You are done!
You can decorate the lapdesk with stickers, art, etc, but remember that it will be getting some heat from the bottom of your computer.