1. Divide the chicken (or hen) halves between two large, resealable plastic bags or shallow glass or ceramic dishes.
2. In a medium bowl, stir together the olive oil, lemon slices, lemon juice, oregano, lemon zest, rosemary, salt, red pepper, and pepper. Rub the marinade into the poultry and under the skin. Seal the bags closed or cover the dishes and refrigerate for at least 4 hours and up to 6 hours, letting the chicken come to room temperature before grilling.
3. Prepare a charcoal or gas grill: Lightly spray the grill rack with vegetable oil cooking spray. Light the coals or heating elements, and let them burn or heat until moderately hot.
4. Lift the poultry from the dish, allowing the herbs to cling to the meat. Discard the marinade and lemon slices.
5. Grill the poultry halves, skin side down to start, and turning several times, for 30 to 40 minutes, until the juices run clear and an instant-read thermometer registers 180°F in the thickest part of the thigh.
6. Serve garnished with the fresh lemon slices and rosemary sprigs.