Okay, here is one way to do it, might not be the best.
Get a 5v or 12v wal wart, and a smart strip. Plug the xbox into the main of the smart strip, the wall wart into one of the controlled sockets. Power the lights with the wall wart.
The other way you can do it is if you desolder the SMDs on the controller and solder your lights to those, but that would be really, really hard, probably need a steady hand, good desoldering tool, super thin iron, and some 30 gauge wire.