Heat the oven to 500 degrees. Combine the lemon juice, 1/2 cup parsley, garlic and some salt and pepper, and rub this mixture all over the chicken. Put the chicken, breast side down, on a rack in a roasting pan and put the pan in the oven.
While it’s roasting, melt the butter or heat the olive oil in a medium skillet or saucepan over medium heat, then add the onions; cook, stirring occasionally, until softened, 10 to 15 minutes. Stir in the remaining parsley and the stock.
After the chicken has roasted for about 20 minutes, spoon some of the onion mixture over it, then turn the bird breast side up. Top with more of the onion mixture, leaving some in the saucepan. Baste again after 10 minutes; at this point the breast should be beginning to brown (if it isn’t, roast a few more minutes). Turn the heat down to 325 degrees, baste again, and roast until an instant-read thermometer inserted into the thickest part of the thigh reads 155 to 165 degrees. Total roasting time will be about an hour and a half.
Remove the chicken from the oven and let it rest for about 5 minutes. Meanwhile, pour some or all of the pan juices into the saucepan with the remaining onion mixture and bring to a boil; reduce slightly if the mixture is thin. Carve the chicken and serve with the sauce.