I have a customer who wants to put 3" Polystyrene outside the sheatheing (1/2" plywood) and then add lath and stone veneer. The framing is 2"x6". So you will have the lath with a browncoat over the insulation and then cultered stone mortared to the lath.
The insulation and lath will be either screwed or nailed through the sheathing with long nails.
I'm concerned with the shear strength and pulling away once they add the cultured stone.