In a covered container, add garlic, lemon juice, black pepper, lemon pepper, and oil. Place the chicken breast meaty side up in the marinade. Sprinkle each chicken breast with salt and then turn over so each one has marinade on both sides. Marinade for thirty minutes in fridge. Heat oven to 450*.
Heat a cast iron skillet on medium heat and lightly brown sweet onion in 1 tablespoon butter, set aside. Add the rest of the butter to pan, add each chicken breast meaty side down. Pour the remaining marinade into the pan, cook for five minutes on medium heat to get them browned on the one side only. Turn chicken over and add the cooked onion to the pan. Place in oven, cook for 15 minutes. Let set for 5 minutes before serving. Spoon onions and juice over each chicken breast when serving.