Split and butter fly the chicken (cut it in half horizontally and open like a book.) Turn the oven to 250 F and place a platter or large dinner plate in the oven to heat.
Heat a large skillet over medium heat. Season the chicken with salt and pepper and "dredge" (or coat) in parmesan cheese. Spray skillet with olive oil. Working in batches, brown the chicken lightly on each side, spray again with oil as needed. Transfer to warmed platter in the oven while finishing the other chicken and the sauce.
Spray the pan with butter spray (about 5 or so sprays). Add the lemon slices and lightly brown. Add the garlic and stir 1 minute. Add the capers if using. Deglaze the pan with chicken broth and add the juice of the other lemon.
Slide the chicken back into the pan and coat with the sauce. Serve with sauce drizzled on top.