SEASON each chicken half with the salt and black pepper, then generously rub every crevice with the olive oil. Put the chicken skin-side down on the lined baking sheet and put the pan on the adjusted rack in the oven. Broil for 15 minutes, until beginning to turn golden.
REMOVE the baking sheet from the oven and flip the chicken over to the other side. Return to the oven and broil for 20 minutes more, or until cooked through, golden brown, and bubbling.
REMOVE the pan from the oven and set the chicken aside. Once cool enough to handle, cut each half into 3 pieces: legs, thighs, and breasts with wings attached. Arrange the sliced potatoes and lemons on the baking sheet. Return to the oven and cook for 10 to 12 minutes, or until the potatoes and lemons begin to brown. Remove the baking sheet from the oven, put the chicken on top of the potatoes and lemons, and pour ½ cup of the Lemon and Garlic Sauce evenly over the top.
RETURN to the oven and broil until the chicken is further browned and crispy, about 5 minutes. Remove the chicken from the pan and drain off any excess liquid from the pan (so that the potatoes can cook to a crisp). Return the potatoes to the oven and broil until crisped and cooked through, 10 to 15 minutes more. Serve the potatoes and lemons with the chicken and the remaining Lemon and Garlic Sauce, either poured over the top or as a dipping sauce.