Preheat oven to 375° Fahrenheit.
Layer lemon rounds in bottom of baking dish.
Sprinkle salt on bottoms of chicken. Flip and place salted-side-down on top of lemon slices.
Using a fork, mix together lemon pepper seasoning, softened butter, salt (if using), and cayenne pepper in a small bowl until well combined.
Rub butter mixture all over chicken. If using chicken thighs, place some butter mixture under skin.
Bake chicken for 25 to 28 minutes (for boneless chicken breasts) or 35 to 40 minutes (for bone-in chicken thighs), or until internal temperature reaches 161° Fahrenheit. Halfway through cooktime, baste chicken with melted butter drippings from baking dish.
Remove chicken from oven and let rest 5 minutes. Internal temperature should rise to 165° Fahrenheit while resting.
Portion chicken onto serving plates. Drizzle with additional melted lemon-pepper butter, sprinkle parsley on top, and serve.
