I've already tested white dye on lanterns & it does make it brighter, I don't have any screenies though, sorry.
Lets see if I can explain why white dye makes it brighter
As I understand it, the way lights work in games is not really the same as RL. what a light does is in effect lighten black-white of the models in the game. so if one was to add pitch black to a game, all the models would basically be coloured black, they'd blend in & you wouldn't be able to see anything. when you add a light source, it creates an area, usually a globe or cone where the models blackness is lowered. sometimes with a tinge of other colours, like the yellow on an unpainted lantern. So, in theory, if we can artificially add more white to the light, we are effectively lowering the black that is in the cone or globe further.
Which leads to the obvious conclusion that if you add black to a lantern you will actually make the light less effective.
Also, this is how Notch (the dev who wrote this lighting code) said it works 8)