How can I feed the right current to a superbright LED with a 3.7V LiPo battery?
I would simply find a voltage regulator or even better, a current regulator that has a low drop-out voltage. In that way, you don't need the sparkfun board and you can control your LED without having to boost it and then regulate it back down. That seems like a lot of effort and wasted energy going through two stages instead of one since your battery can handle the voltage requirements of the LED.