Just google "lap desks with storage".
Then narrow down to just images until you see something you like and can use directly.
Or modifiy to meet your requirements.
Or use as a template (modified or otherwise) to build yourself.
May be easier to just put the tray in place and then the laptop on top versus lifiting up some "storage", removing the laptop, setting the laptop aside, assembling the tray/desk, and then putting the laptop on top then to be opened, connected, etc....
Certainly do not know your full situation or requirements - no judgements being made on my part.
Simplicity is the key I would think.