Wait...Danger, Danger, Danger...
As the Earth moved farther from the Sun, wouldn't the L2 point move closer and closer to the earth?
Eventually, I believe that if the Earth got to far from the sun, then the L2 point would be located somewhere inside of the Earth itself...At that point the Earth will have achieved an escape velocity and will eventually "spin out of the solar system! How Horrific a prospect...
Of course we could then just move our large gravitational body to L1...
See what happens when you try to stretch one's technological knowledge beyond its limits...
Scott Evil