Place chicken breasts on a plate. Season chicken with a little salt and pepper and lightly dust with flour.
Beat the egg white with milk in a shallow bowl. Toss breadcrumbs and Parmesan cheese together in another shallow bowl.
Dip each piece of chicken in egg white mixture, coating both sides and dredge in bread crumb/Parmesan mixture and set aside. Continue with the rest of the chicken.
Coat a large nonstick pan with cooking spray. Add 1 tablespoon butter and 1 teaspoon olive oil and melt over medium-high heat. Add the 4 breaded chicken breasts, cover the pan, and cook for 4-5 minutes until browned and crispy. Turn chicken over, add remaining tablespoon butter to pan, and swirl around to melt. Cover pan, turn heat down to medium, and continue to cook for 4-5 minutes until browned and cooked through. Remove chicken to a serving plate.
Add the wine and lemon juice to the pan and heat for about 2 minutes over medium heat until pan sauce is slightly reduced.
Pour sauce over chicken and serve.