Stir together the flour, 2 teaspoons of the salt and 2 teaspoons of the pepper in a shallow bowl; reserve 1 tablespoon of this flour mixture and set aside.
In another small bowl, stir together the remaining 2 teaspoons each of salt and pepper and the lemon zest until combined. Sprinkle the chicken evenly with this lemon-pepper mixture.
Dredge the chicken in remaining flour mixture to coat. Set aside.
Thinly slice one of the lemons and cut the other lemon into wedges; set them all aside.
Heat 2 tablespoons of butter and 2 tablespoons of olive oil in a large nonstick skillet over medium-high heat until bubbly. In two batches, add the coated chicken to the skillet. Cook until the chicken is browned on both sides and reaches an internal temperature of 165°, 4 to 6 minutes per side (add the remaining 2 tablespoons olive oil in between batches, if needed). Transfer the chicken to a serving platter and tent with foil to keep warm. Remove the pan from the heat to let cool slightly.
Reduce the heat to medium and return the skillet to the heat. Add the remaining 2 tablespoons of butter and the reserved 1 tablespoon of the flour mixture to the skillet. Cook, stirring constantly, until the flour is toasted, about 1 minute. Add the garlic, lemon slices and the chicken broth to the skillet. Cook, stirring occasionally, until the sauce is bubbling and slightly thickened, and the garlic is lightly browned, 2 to 3 minutes. Spoon the sauce and sliced lemons over the chicken. Garnish with parsley and serve with lemon wedges, if you like.
