Prepare the chicken breasts as directed into thin cut pieces that are pounded to 1/2 inch. If you want to marinate for extra flavor do so for a few hours in a little lemon juice, salt, pepper and garlic.
Mix flour with some salt and pepper in a bowl.
Heat 2 tbsp butter plus the oil in a skillet over medium high. Once hot, add the chicken pieces and let cook on one side until browned, a few minutes. Flip and brown the other side until the chicken is fully cooked.
Remove chicken and set aside. Add the wine and scrape any brown bits off the pan into the sauce. Let the wine boil for a minute to burn off the alcohol.
Add the broth and lemon slices. Let the mixture reduce by half, then add the capers, butter, and the lemon juice.
Place chicken back into the sauce and sprinkle with parsley. Adjust the sauce seasoning and serve. The flour you dredged the chicken in will help to thicken the sauce.
Toast and butter the sourdough and serve along side the chicken.