Slice and juice the lemons. Set juice aside. Season the chicken with the lemon pepper.
Set up your breading station with 3 bowls. Add flour, bread crumbs and beaten eggs each into its own bowl.
Holding a chicken tender in one hand, dredge it through the flour, then dip it in the eggs and shake off excess. Drop chicken in the bowl with the bread crumbs. Using your other hand, gently press bread crumbs to adhere. This keeps your hands from becoming gummed up with egg and crumbs. Repeat this twice for each tender.
Add 1/4 cup butter and olive oil to a cast iron skillet or frying pan over medium-high heat. When butter has melted, sauté the breaded chicken tenders for 4-5 minutes per side, or until golden brown. Remove pan from heat and transfer tenders to serving platter and cover with foil to keep warm.
Melt remaining 2 tbsp of butter in the pan and add 2 tablespoons of flour. Cook for 2 minutes over medium high heat, scraping up the bits left from cooking the chicken. Whisk in the chicken stock and lemon juice to form a nice sauce. Add the Italian seasoning and simmer on low heat for 2 minutes. Taste, then season with salt and pepper if necessary.
Plate the chicken, spoon sauce over top, and serve.
Chicken tenderloins are the short pectoral muscles located underneath the breasts. If you're unable to find fresh chicken tenderloins, you can use tenders. Tenders are simply long strips of boneless skinless chicken breast.