Simply, no you cannot dye hair for better laser hair removal results. People have thought of this and tried, and had no effect. The issue is that the hair removal laser targets the hair follicle itself. The actual bulb where the hair grows out from. There is no way to get the dye into the follicle to be targeted by the laser, as the hair shaft only gets the dye and changes color. (This is why you can tell when people have dyed hair - the "roots" so to speak as to where the hair comes from, doesn't change color or take up the dye.)
"This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."