Preheat the oven to 200 degrees. This will keep chicken cutlets warm as the sauce is made in the same pan.
Cut the chicken breasts into cutlets, about 1/4 of an inch thick. Pat them dry with paper towels.
Wash the lemons and cut one of them in half. Then, cut both halves into thin half-moon shaped slices. Either juice the other lemon, for a total of 1/4 to 1/2 cup of lemon juice, or measure out store bought lemon juice.
Season the cutlets with salt, pepper and other seasonings as desired.
Heat a little vegetable oil in a heavy-bottomed skillet over medium-high heat.
In a medium bowl, dredge two to four cutlets through the flour. When the pan is hot, add them to the pan.
Cook for 2 and 1/2 minutes on each side, until lightly browned. Do not crowd them in the pan.
When the first batch of cutlets is done, remove them to a baking dish and put them in the preheated oven.
Continue dredging and pan frying the cutlets until they have all been cooked, adding oil as required. Remove the cutlets, as they finish, to the pan in the oven.
Add the garlic to the pan and, 10 seconds later, add the chicken stock and 1 tablespoon of butter. Simmer until the liquid reduces by a half, around 4-5 minutes.
Add the lemon juice, lemon slices, white wine if using and the rinsed capers and continue simmering until the sauce is reduced by half.
Add the rest of the butter and stir until melted.
Remove the chicken from the oven and pour any juices into the skillet. Add the parsley to the skillet.
Taste the sauce and add salt or pepper as required to taste.
Pour enough sauce over each cutlet and serve by itself or serve over rice or pasta.