Heat 2 tablespoons butter and 2 tablespoons of oil in a large skillet over medium high heat. Dredge chicken breasts in the flour, season each side of the chicken breasts with lemon-pepper seasoning. Place the chicken breasts in the skillet. Cook for about 5-8 minutes on each side or until cooked throughout and no longer pink inside. Remove from the skillet and set aside on a plate.
Turn the heat to medium low. Add broth, juice from lemons, heavy cream, and capers. Bring the sauce to a boil, reduce heat to medium low. Taste the sauce and season with salt and pepper as needed.
Allow the sauce to cook and bubble for about 3 mins. Return chicken breasts back to cream mixture. Cover and cook on medium low for 15 minutes or until chicken breasts are cooked through.
While chicken breasts are cooking, make pasta according to package directions. Serve chicken and sauce over cooked noodles.