LINbus seems overkill for a few LEDs... why not just a small MCU running very slow serial? Or even MIDI? 10m would be pushing TTL level serial but you could always try it with the cable you have. There's always the simple PPM/PWM used in cheap RF remotes although given you have an input as well you could jsut use that for the LED's, and a single wire for the button, that way comms is oneway.