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You could probably get away with a tiny LED light and a battery. Maybe even get a rechargeable mini LED flashlight?

But for something identical in the picture you'd need a lot of lights.
 
I went to Wal-Mart and found some GE 12" LED strip with a wireless trigger and it works pretty well and it's really simple. Just adhere the lid to the light (I have them pointed down at the top for a more uniform glow).. then attach that to the wall.

The only issue is that the lid isn't flat with the wall, but that's not really a problem with where I wanted to mount it anyway (hanging on a door).
 
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