When you have laser hair removal, the laser flash pumps a ton of energy into the hair follicle which essentially roasts the shit out of the hair follicle so it dies, usually it will re-product hair at some point but very thin, wispy white hair if any at all.

You need to shave your hair for laser hair removal since you don't want a long melting chunk of hair on your body that will cause serious burns. Hair dye will not color the root base of the hair meaning that heat energy will not travel down to the base as well and probably just destroy the pigment dye instead of the hair itself.