I'd be surprised if the lacquer holds up; I'm guessing it'll wear away pretty quickly (especially with roundwounds, but even flats will abrade it).
I'd probably use a good coating epoxy mixed with opaque black tint - there are plenty of threads detailing which epoxies do well at coating fretless fingerboards boards. I've used West System and System Three Mirror Coat or Clear Coat (I don't remember which; it has been a while since I did one), but searches in this forum should yield epoxy and tint recommendations.