Yes, just dump this thought process now. There is nothing there to go after. Every time you convert energy, you lose some.
Nobody here is being cynical, but you have to think about the numbers. Even a good solar panel is only about 20% efficient, so only 20% of the light that hits it from the led is going to be captured. The other 80% is lost. Why not use the other 80% of the light to do what the LED is meant to do, and then use a smaller led which uses less power. It will easily be more efficient than trying to capture it and convert it back into electricity.