If you are talking about a lighting device, and not an e-reader, then I can recommend Nitecore products that can do 1 lumen at the lowest setting. I use them myself.
For example, this is a good little lamp for night-reading that you can carry around in keybundle
http://flashlight.nitecore.com/product/tube
And this one is good for everything, as a bicycle light, in the yard, and indoors
http://flashlight.nitecore.com/product/mh12gt
For the latter one you have to add a little white filter to disperse the light (otherwise it emits a narrow sharp beam, it's a "thrower" type of flashlight). The former one emits an appropriately dispersed light, it's perfect as it is.
The only additional problem with these lights is to place them solidly, hang them or fix them so they are at a perfect angle.