Zest one whole lemon, then cut lemon in half. Place lemon halves in chicken cavity.
Place lemon zest in a small bowl with the butter. Microwave until completely melted (approx 1 minute)
Pour melted lemon-butter all over chicken, use your fingers to spread the butter evenly.
Sprinkle salt and pepper liberally all over the chicken. Place chicken breast-side down on cast iron skillet.
Slice the other lemon into thin slices. Place lemon slices around the chicken, then place carrots, garlic cloves, and fresh thyme all around the chicken.
Lower the oven temperature to 400 degrees F, then place skillet in the oven. Leave the chicken untouched for at least 50 minutes.
Roast until internal temperature on the thickest part of chicken thigh reaches 165 degrees F.
Let the chicken rest for about 15 minutes before carving.