How Long Would It Take LightSail 2 To Escape From the Earth?

 One can compute LightSail 2's gain in energy over time and estimate the average rate at which it will gain energy.

This average rate appears to be linear and allows one to estimate how long it would take for the light sail to acquire enough energy to escape from the Earth's gravity well. The answer is 6.4 years.

The model used was overly simplified neglecting the Earth's shadow and didn't take into account the need to raise the height of perigee to avoid atmospheric drag. As the Earth moves about the Sun in its orbit the direction of sunlight will slowly change.