Pound chicken breasts with meat mallet to a uniform 1/3-inch thickness. Season on both sices with salt and pepper. Place flour on a large plate and dredge chicken lightly in the flour, shaking off excess.
Meanwhile, in a large saute pan over medium-high heat, melt the butter and oil until it sizzles. Add the chicken breasts and saute, turning once or twice, until almost cooked through and chicken is golden on both sides, about 3 to 4 minutes per side. Remove chicken and set aside.
Whisk the 3 tablespoons flour into drippings in pan and cook, stirring for 1 minute. Whisk in lemon juice and chicken stock. Bring to a boil, then reduce heat to a simmer. Return chicken to pan to finish cooking until juices run clear, and let sauce reduce until thickened. Season to taste with salt and white pepper.
Spoon sauce over chicken to serve Garnish with chopped parsley and lemon slices. Serve over noodles or rice (Katie likes Basmati rice).