Trim fat from each chicken breast. Place one chicken breast between two layers of plastic wrap; pound with the flat side of a meat tenderizer or the back of a large metal spoon until ¼ inch thick. Do this with each chicken breast and set them aside on a dinner plate.
Heat 3 T olive oil over medium heat in a large, non-stick skillet. Since all the chicken will not fit into the skillet at once, I like to use two skillets to speed up the cooking process.
In a shallow bowl, using a fork, beat the eggs together with Dijon mustard and Worcestershire sauce. Place breadcrumbs on a serving platter or dinner plate and spread them out. Dip each chicken breast first into the egg mixture and then into the breadcrumbs. Place each chicken breast into the hot oil and cook about 6 minutes on each side. Once cooked, remove to a plate and cover with foil to keep warm.
After all of the chicken is finished, drain any excess fat from the skillet/s. Add in the chicken broth, lemon juice, parsley, and capers. Bring this to a boil while scraping all of the browned bits from the bottom of the pan. Add the lemon slices and remove from the heat.
Remove the foil from the platter of chicken and spoon the sauce evenly over top. Serve immediately.