Preheat the oven to 450 degrees.
Spatchcock your chicken - using kitchen scissors, cut the backbone out of the chicken. (To flatten the breast you'll need to cut through the cartilage).
Season the cavity with salt and pepper, then transfer the chicken to a cast iron skillet laying the chicken breast side-up.
Generously season the skin with more salt and pepper.
Toss the potatoes in a bowl with melted butter, olive oil, salt, and pepper, then arrange them around the chicken in the skillet.
Roast the chicken 30 to 45 minutes, or until a thermometer inserted into the the thigh reads 165 F
Check after about 20 minutes, and toss the potatoes around
Remove the skillet from the oven, and sprinkle with the thyme and zest, and drizzle with the lemon juice.
Allow the chicken to rest 10-15 minutes before carving and serving.