Heat 2 tablespoons of the butter in a skillet over medium heat. Add the bacon and cook until it begins to brown. Add the onion, celery, and garlic, and cook until the onions are translucent, stirring regularly.
Remove the skillet from the heat and add the bread crumbs, apple, tarragon, basil, chives, parsley, 1/2 teaspoon salt, a few generous grindings of black pepper, and the lemon zest. Mix well to combine. Return the skillet to medium heat and stir for 2 minutes to further combine the flavors. Remove from the heat and let the stuffing cool in the skillet. (Stuffing can be made up to this point a day ahead and stored in the refrigerator). Beat the lemon juice with the eggs and pour over the breadcrumbs. Mix very well to coat all the ingredients with the egg.
Pre-heat the oven to 350°F. Melt the remaining 2 tablespoons butter and combine with the olive oil in a small dish.
Fill the chicken with the stuffing, pack it fairly firmly (there may be a small amount left over). Cross the legs and tie with kitchen twine to help contain stuffing. Brush the chicken generously all over with the butter-oil mixture and salt and pepper the bird generously on all sides.
Transfer the chicken to a rack set in a roasting pan and roast in the center of the oven for 1 3/4 hours. After 30 minutes, brush the top and sides of the chicken with the butter-oil mixture. For the remainder of the cooking time, brush the bird every 20 minutes or so with the fat accumulated at the bottom of the roasting pan once the butter oil mixture runs out.
Remove the roasting pan to the stove top and transfer the bird to a cutting board designed to catch the juices. Let the chicken rest for 10 minutes.
Meanwhile, spoon off some of the fat from the roasting pan. Set the pan over medium heat. Add the stock and simmer until the liquid is reduced by one-third, about 5 minutes, scraping up any brown bits stuck to the bottom of the pan. Carve the chicken and divide the stuffing and chicken among warmed serving plates. Pour any juices on the cutting board into the roasting pan to combine. Spoon pan juices around each portion and serve.