He's talking about the sensors and solenoids only. The rails still get power from the track as they should. Normally, the sensors and solenoids get power from the same source. If you open the small panel under the sensors, you'll see red and black wires soldered to the rails. Those are powering the lane change electronics and flippers. Desolder those and connect them to your external power source. Make sure it's not over 15v, and has enough amps for all your lane changers. No more than 6 amps should be needed.
I'm hesitant to say that this will fix the problem, though. Unless you notice severe power issues around/at the problematic lane changers, such as magnet cars bogging down and going slowly, then it's probably not a power issue so much as a mechanical one. If you can put the lane changer right on the power base and it still has issues, then it's clearly not a power problem.
What the problem actually is, will be the tricky part to nail down. Have you tried vacuuming the slot where the sensor is, to make sure no dust or debris is clouding the sensor? Can you feel any resistance in the flipper motion? If you take the XLC out and tilt it gently from side to side, will both flippers freely and easily slide back and forth? If not, then there's a physical obstruction that needs to be taken care of. It could be in the solenoid, the sliding arm bit, or even the bottom of the slot where the flipper rubs underneath.
If a flipper stops responding completely, no matter what, then it could be a damaged sensor. Stock slot.it guides are deep enough to rip off the little sensor bits in the rare lane changer that has a proud-sitting sensor. This is more common in the Pit Lane Game sensor, but has been known to happen to lane changers as well. If you're worried about that, just file the bottom leading edge of the guide on slot.it cars so that the blade skips over sensors rather than rips them off. This is especially important for any stuck down magnet cars.