How do I install a manufactured stone surround on a zero clearance fireplace?
If you need to overlap, the cement board could do it in a more continuous manner, making it easier to thinset the stone.

Usually its either/or with lath vs cement board.  Are you going to use both? 

Properly secured board (8in OC) is sufficient for manufactured stone for a veneer and using thinset.  Thicker stone using a mortar might want the lath support.