Pat the boneless skinless chicken breasts dry with paper towels, then season both sides evenly with the salt and black pepper.
Place the all-purpose flour on a plate and lightly coat each seasoned chicken breast in the flour, shaking off any excess.
Heat 2 tablespoons of the olive oil in a large skillet over medium heat, then add the floured chicken breasts in a single layer.
Cook the chicken breasts for 4 to 5 minutes per side, or until they are golden brown on the outside and cooked through, then transfer them to a plate and set aside.
In the same skillet, add the remaining 1 tablespoon of olive oil and the unsalted butter, stirring until the butter is melted and starts to foam gently.
Add the minced garlic to the skillet and cook, stirring constantly, for about 30 seconds until fragrant, being careful not to let it brown.
Pour the low-sodium chicken broth and fresh lemon juice into the skillet, then add the lemon zest, dried oregano, and dried thyme, stirring to combine and scraping up any browned bits from the bottom of the pan.
Bring the sauce to a gentle simmer and cook for 4 to 5 minutes, stirring occasionally, until it reduces slightly and begins to thicken.
Return the cooked chicken breasts and any accumulated juices to the skillet, nestling them into the lemon sauce.
Lay the fresh lemon slices on top of the chicken breasts, then spoon some of the sauce over the chicken.
Reduce the heat to low and simmer the chicken in the sauce for another 5 to 7 minutes, turning once and basting with the sauce, until the chicken is tender and well coated.
Sprinkle the fresh parsley over the Italian Lemon Chicken, then taste the sauce and adjust the seasoning with a little extra salt or black pepper if needed before serving.