Special equipment: a waffle iron (for Lemon and Walnut Waffles)
In a bowl large enough to fit the chicken, combine the water, lemon juice and halves, salt, and sugar. Whisk until salt and sugar are dissolved. Add the chicken to the bowl, cover and refrigerate for at least 6 hours, or overnight. If the brine does not fully cover the chicken, rotate the chicken halfway through the brining process. Preheat the oven to 350 degrees F.
In a small bowl add half of the BBQ Rub and the butter. Mix until well combined. Refrigerate for a few minutes if the butter begins to melt after mixing. Remove the chicken from the brine and pat dry with paper towels. Use your fingers to gently release the skin from the flesh of the breasts and legs. Spread the butter mixture evenly under the skin and over the breast and legs. Pat the remaining BBQ rub mixture all over the bird. Transfer the chicken to a roasting pan fitted with a roasting rack and bake until golden and the juices run clear, basting frequently, for about 1 hour 15 minutes. Remove the chicken from the oven and raise the oven temperature to 450 degrees F. Baste the chicken thoroughly with the drippings in pan, return to the oven, and let bake until the skin is brown and crispy, about 15 minutes. Remove from the oven to a cutting board and let rest for 10 minutes before cutting. Carve the meat and arrange on a serving platter. Serve with Lemon and Walnut Waffles, if desired.
Combine all the ingredients in a small bowl and set aside.
Preheat the oven to 225 degrees F.
In a large bowl sift to combine the flour, baking powder, 2 tablespoons of the sugar and salt. In small bowl whisk the egg yolks until smooth, then add the milk, vegetable oil, lemon extract, and lemon zest. Make a well in the center of the dry ingredients. Pour in the liquid ingredients and gently stir the batter, with a wooden spoon, until just combined. Be careful not to overmix. You can use a hand beater or a stand mixer on low speed, if desired.
In a very clean bowl, whisk the egg whites until foamy. Add the remaining sugar and beat until soft peaks form. Gently fold the whites into the batter. Pour about 1/4 cup to 1/2 cup batter into an oiled waffle iron, sprinkle with walnuts, then close the iron. Cook until golden brown, about 5 minutes, depending on waffle iron settings. Transfer to a serving platter and keep warm in a low oven. Repeat with remaining batter. Serve warm with maple syrup.