When ready to grill, prepare a hot charcoal fire on 1 side of a grill (or turn a gas grill on low heat). Spread ¼ of the coals across the other side of the grill. Place the chicken on the cooler side, skin side up. Cook for 12 to 15 minutes, until the underside is golden brown. Turn the chicken skin side down and cook for another 12 to 15 minutes, until the skin is golden brown and the chicken is cooked through. Place the lemon halves on the cool side of the grill, cut side down for the last 10 minutes of cooking. Remove the chicken to a plate or cutting board, cover with aluminum foil, and allow to rest for 5 minutes. Cut in quarters, sprinkle with salt, and serve with the grilled lemon halves.