Wash chicken parts and pat dry. Arrange the chicken in single layer in a large shallow dish.
In a small bowl, whisk together lemon peel, lemon juice, garlic, dried thyme, salt, and pepper. Spoon lemon mixture over chicken; refrigerate for 3 to 4 hours, turning several times to coat well.
Remove chicken from marinade and drain well, reserving marinade. Arrange chicken in a 2-quart shallow baking dish. Brush with melted butter. Bake at 425° for 25 minutes. Brush some of the reserved marinade on the chicken and bake for about 30 minutes longer, basting several times. Chicken should be browned and cooked through.
Garnish chicken with lemon slices and sprinkle with chopped parsley. Boil remaining marinade for 1 minute and spoon a little over the chicken just before serving, or serve separately. Serve with hot cooked rice or noodles.