Place each chicken piece between 2 sheets of waxed paper; flatten to 1/4-inch thickness using a meat mallet or a rolling pin.
Combine flour and pepper, stir well.
Dredge chicken in eggs and then in flour mixture, shaking off excess flour; set chicken aside.
Heat butter and oil in a heavy skillet.
Cook chicken in skillet over medium heat about 4 minutes on each side or until golden brown.
Remove chicken to serving platter; keep warm.
Add mushrooms and 1/4 cup water to pan drippings, cook over medium heat, stirring often, about 3 minutes.
Spoon mushrooms over chicken.
Add wine and lemon juice to skillet; heat thoroughly.
Pour sauce over chicken; sprinkle with parsley.