Does a graphical driver chip exist for this project?
I have no idea if there is a chip or not, but I doubt it.

But then, why do you need one?

You already know how to communicate with the screen, so why not off-load those functions on to another Arduino (make your own small ATMega328P based board to do it) and then communicate with that through whatever means you like from your Leonardo?

You don't need a dedicated chip to do what you can quite easily program an Arduino to do.