In a wide, shallow bowl, beat the egg. Place the bread crumbs in another wide, shallow bowl.
In a large nonstick skillet over medium heat, heat the oil.
One at a time, dip each chicken cutlet in the egg and then into the breadcrumbs.
Add the cutlets to the hot skillet and cook for about 3 minutes on each side and remove to a plate.
To the hot skillet, add the lemon juice, mustard, and butter, stirring well after each addition to scrape any bits off the bottom of the skillet. Pour sauce over the chicken and serve.