Combine thyme, salt, and butter until evenly mixed. Loosen skin away from breast, legs, thighs, and wings. Insert pats of butter underneath loosened skin. Make sure butter mix is evenly spread across the entire underside of skin. On outer skin, liberally apply lemon pepper seasoning. Use a hot grill and the indirect cooking method. Place a drip tray under the rack. Oil the rack and place chicken directly on rack, breast side up. Cook about 1 1/2 hours or until juices run clear.