How to Make It
Preheat the oven to 450°. In a small bowl, blend the 1/2 stick of butter with the thyme and 2 tablespoons of the lemon juice. Season with salt and pepper.
Season the chicken cavity with salt and pepper and tuck the lemon inside. Spread one third of the lemon-thyme butter under the skin of the breasts and thighs. Rub the remaining butter all over the chicken and season with salt and pepper.
Set the chicken breast side up in a large cast-iron skillet. Roast for 40 to 45 minutes, until an instant-read thermometer inserted in the inner thigh registers 160°. Transfer the chicken to a carving board and let rest for 10 minutes.
Meanwhile, skim off all but 1 tablespoon of fat from the pan juices. Stir in the remaining 1 tablespoon of lemon juice and cook over moderate heat until hot, 1 to 2 minutes. Remove from the heat and stir in the remaining 1 tablespoon of butter. Season with salt and pepper.
Carve the chicken and transfer to a platter. Spoon the pan sauce on top and serve.