Cut the metal lath to size and set it aside. Use a hammer drill to pre-drill holes into the mortar. Drive in one concrete screw or nail every 6" to 8" to hold the lath securely in place on the brick façade. Make sure to drive the nail or screw into the mortar and not the brick, as the brick may crack.
Create a scratch coat by mixing a batch of type M mortar until firm but still moist -- a creamy consistency is important for the mortar to bond properly. Use a square-end trowel to apply a thin layer (1/2" to 3/4") of mortar over the wire lath. Cover small areas, about 4 to 5 square feet, to ensure that the mortar doesn't set up too quickly. Work with upward strokes with the trowel's leading edge (top edge) held slightly away from the surface, creating an angle that will help push the mortar into the lath. Continue in this manner until the entire area is covered.
Starting with the outside corner pieces, wet the backs of each stone with a damp sponge. Next, apply a moderate layer of mortar around the outer edge and then press the stone firmly against the scratch coat. You should see some mortar squeeze out. Wipe off the excess.
Work your way toward the center, stacking the stone as you go. As you work your way in and up, make cuts as needed using the angle grinder and mason's hammer.
At the fire-box opening, use a scrap piece of 2x4 as a temporary brace to hold up the stack stone until it cures. Cut a piece to the width of the opening and two more pieces to the height of the opening, minus 1-3/4". Hold the first piece up to the top of the opening, then place the other two into position to hold it up.
Once all the stone is applied, wipe off any excess mortar on the stone. After the mortar has cured, remove the scrap wood.
Note: Unlike veneer stone, stacked stone does not have mortar joints to fill.