I'd also, while we're on this topic, to consider cocoa beans be used to make '2 brown dye per bean', as well as lapis being used to make 2 blue dye.
The stone, lapis, in real life, is used (or was) to make oil based coloring for paints and dyes. You don't (or didn't) rub the stone itself against things, because it's not a 'chalky rock', it's a solid stone.
So in these terms, it seems only natural you 'grind' it into dye (and again, why not cocoa beans doing the same thing?)
I think blue dye would be a good idea. I mean, there is LIME dye, MAGENTA dye, but no blue dye? It makes no sense. I would really like to dye my leather armor blue. True, it can be used to dye sheep, but they just give u that wool, which cannot be crafted into dye.