Place chicken breast halves between sheets of plastic wrap. Lightly pound with bottom of heavy skillet or rolling pin to flatten slightly.
Whisk together the mustard and eggs in a shallow dish until well blended. Spread the bread crumbs evenly on a sheet of waxed paper. Dip the chicken breasts into the mustard mixture, using a fork to hold the chicken. Then coat with crumbs, patting to make the crumbs adhere.
Heat 2 tablespoons of the oil in a large skillet over medium heat. Add half the coated chicken breasts in a single layer; sauté for 5 minutes or until lightly browned. Using tongs, turn chicken over; cook for 5 minutes more or until internal temperature registers 170°F on instant-read thermometer inserted in the chicken. Transfer chicken to platter; keep warm. Repeat with remaining oil and chicken.
Drain any excess fat from the skillet. Add the chicken broth, lemon juice, capers and salt. Bring the mixture to boiling, scraping up any browned bits from the bottom of the skillet with a wooden spoon. Add the lemon slices and chopped fresh parsley. Remove the skillet from the heat.
Spoon the lemon sauce over the chicken breasts on the platter. Serve immediately.