Preheat the oven to 200 degrees F (95 degrees C). Place a serving platter into the oven to warm.

Season chicken breast pieces with salt and pepper and dredge them in flour. Shake off excess flour. Heat vegetable oil in a skillet; pan-fry the chicken pieces until golden brown on both sides, about 3 minutes per side. Work in batches and do not crowd skillet, adding oil as needed. Place chicken pieces onto the warmed platter in the oven. When finished with all of the chicken, drain most of the oil from the skillet, leaving a thin coating on the surface of the pan.

Cook and stir minced garlic in the skillet until fragrant, about 20 seconds. Pour in chicken broth; scrape and stir any brown bits from the bottom of the skillet. Stir in lemon slices and bring the mixture to a boil. Let cook, stirring occasionally, until the sauce reduces to about ⅔ cup, 5 to 8 minutes. Add lemon juice and capers; simmer until sauce is reduced and slightly thickened, about 5 minutes more. Drop butter into the skillet and swirl it into sauce by tilting the skillet until butter is melted and incorporated. Add parsley; remove from heat and set aside.

Arrange chicken medallions on serving plates and spoon sauce over each portion to serve.