Heat Grill: Heat your grill to high (400-425F degrees) with a direct heat zone.
Prep: Slice the rack of lamb into chops. If there is an excessive fat cap, trim some of the fat away.
Make Marinade: In a small bowl, combine the shallots, garlic, thyme, olive oil, juice of one lemon, white wine vinegar, salt, black pepper and sugar.
Marinate: Spread the marinade onto both sides of the lamb chops. Let marinate for 30 minutes while the grill heats.
Grill: Place the chops on the grill and cook 3-5 minutes per side or until the internal temperature reaches your preferred doneness. The USDA recommends 145F degrees.
Rest: Let the meat rest about 5 minutes before serving.
Notes
If you're lucky, you may be able to find pre-cut lamb rib chops. You can use those instead of a whole rack of lamb.