The fireplace has a stone facade as shown below. It may be faux stone, I'm not sure - the individual stones are 1/2" tall, and 1-1/2 to 3 inches wide. Viewing it from the side and measuring, it appears to be about 5/16" thick. Underneath it I believe there are ordinary drywall and studs. My stud detector was able to locate the studs without much trouble on the 1-1/2 inch setting (marked with electrical tape below), and I confirmed by finding the nails in the studs with the metal detector setting.
I've never worked with stone before. My plan was to rent/buy a hammer drill and some masonry bits. I start with a small pilot bit (like e.g. this carbide hammer drill bit), go slowly, wear safety glasses, and then gradually enlarge it until I reach the diameter of the lag bolts that I want to use (probably 5/16" diameter). Then I use my regular drill to get through the drywall and the stud. I use a slightly smaller diameter like 1/4" for the studs so that the bolts can bond with it. The lag bolts should probably be 3" long to account for the mount's wall plate (1/4"?), the facade (5/16"), the drywall (1/2"?), and finally 1-1/2" or so into the stud.
What I'm not sure about here is: is this the appropriate technique for this kind of facade? I feel like this is probably faux stone and very thin and that I'm probably being excessively cautious, but I don't want to crack or crumble it, or destroy my drill or drill bits.
I consulted these earlier posts: What type of screws and drill bits should I use to mount a mantel over faux stone?, What is the right drill bit for concrete or stone walls?