UPDATED: Upgraded the Caddy to have pegs in the corners and holes in the cap pieces. The caps now can snap into place and are probably fine without any glue. But even if you'd still like to glue them, now they are a cinch to place in exactly the right place.
A classy lithophane display and matching storage caddy that's easy to work with and customizable to suit whatever location and lighting solution you may have in mind...
Use CenterA with a USB powered LED strip: a cheap, easy way to get bright, even lighting when your display will be more permanent and can remain plugged into a power source. Power is routed through and secured in place by the back of the display, limiting you to using only three lithophanes. This is the exact LED strip I used.
Use CenterB with battery powered string lights: cheap and portable but likely not to be as bright in a lit room. It's a very neat parlor trick to be able to carry around the display and show it off like a glowing, magical artifact though. And with this option, all four sides can be used to display lithophanes. This is the set of lights I used. I removed the front cover and sanded away any hinges or latches to get the width as small as possible, it doesn't need to be super secure or waterproof in this usage.
If you want to go a different way, maybe a small handheld LED lantern or set on top of a lamp...just use the simple, bare Baseplate file or no bottom piece at all.
And once you have a great, decorative lithophane display on your mantel or dresser, you need a way to keep more lithophanes nearby that isn't just a precarious pile or repurposed cardboard box, so I designed a companion caddy with the same styling that can hold an additional thirteen 90mm x 90mm x 3mm lithophanes.