Hi Julie! Thanks for your post, and thanks John Gerlach for your reply. That's exactly what we were going to recommend. Either a 2-pack of light strips or a 2-pack of Pico LEDs would work. To power everything, you could add a USB cable and use a spare iPhone/iPad type charger to power everything from wall power.
This looks like a really cool lamp design! Please keep us posted on how you light it up.