Prep Garlic Rosemary Rub: whisk together Garlic Rosemary Rub ingredients in a small bowl.
Prep Lamb: Cut 10-12 1-inch slits in the lamb and push a slice of garlic into each one. Rub all over with the Garlic Rosemary Rub. Let marinate at least 2 hours or overnight.
Prep Mint Yogurt Sauce: combine Mint Yogurt Sauce ingredients in a medium bowl. Cover and place in the refrigerator for later.
Room Temp + Prep Grill: Leave lamb out and allow it to come to room temperature before grilling (if you are only marinating your lamb for 2 hours you can simply leave it on the counter and let it come to room temp while it marinates). Season lamb with salt and pepper. Preheat grill to 350 degrees F. and ensure the grill grates are clean.
Grill Lamb: Place prepared lamb on the grill grates over indirect heat and close the lid (no need for a drip pan, there won't be many drippings). Keep grill temp between 325-350 degrees F. Let cook until the internal temperature of the lamb reaches 128 degrees F. for a medium-rare finish (use an internal meat thermometer).
Rest: Remove from grill and let rest 10 minutes before slicing - the internal temp will continue to rise as it rests reaching between 130-135 degrees F. at the time of slicing.
Notes
Lamb Temps: medium-rare 130-135 degrees F.; medium 135-140 degrees F.; medium-well 140-145 degrees F.
Cook Time: there are a lot variables that go into total grill time such as thickness of lamb, outdoor temp, wind, etc. That being said,15-20 minutes per pound is pretty usual, but track the internal temperature with an instant read thermometer or probe to be sure.