I made a slew of origami lanterns for a friend's wedding a few years back, and it seemed only right to add lights to the design. After all, they are lanterns! As I have no desire to burn my apartment down, I decided to use some flickering LEDs from Evil Mad Scientist that give the appearance of a candle, without the paper-eating flame. You can use whatever LEDs you like.
As these were made to look like Chinese lanterns, I chose red and yellow for my colors. You can obviously make these in different colors/shapes/sizes and customize to your heart's content.
You'll find me telling you to experiment a lot, because it's fun to tinker, and because it allows you to make this project your own. I want to see pictures of what you've modified!