Rough up the entire surface of the ledge wall where you will be applying the cultured slate, using rough grit sandpaper. Wipe the surface clean. Find the studs in the wall using the stud finder and mark them clearly.
Spread lath across the area to be covered and attach it in place using 3-inch galvanized wood screws with plastic disc washers. Drill the screws into each stud, spacing them every 6 inches. Overlap the lath at all seams by 4 inches.
Spread mortar across the lath at a depth of a 1/4-inch. Let the mortar dry for two hours. Scratch up the entire surface of the mortar using a metal rake. Let the mortar dry for 48 hours.
Cut slate pieces with a saw prior to installation if necessary for a good fit. Apply 1/4 inch of mortar to the back of each cultured slate piece. Apply them from the top of the wall to the bottom. Hold the slate in place for one minute before releasing. Let the pieces dry for two hours. Fill in the areas between the stones with grout if desired. Let the pieces dry for 48 hours.