Cut chicken breasts horizontally into four cutlets and season both sides with salt, pepper, and garlic powder.
Dredge seasoned chicken cutlets in flour, shaking off excess.
Heat olive oil and 1 1/2 tablespoons butter in a large skillet over medium-high heat until butter melts.
Pan fry chicken cutlets until golden brown and cooked through, about 4-5 minutes per side. Remove chicken and set aside.
Add chicken broth, lemon juice, lemon zest, and remaining 1 1/2 tablespoons butter to the same skillet.
Bring mixture to a simmer and cook until sauce begins to thicken, about 2-3 minutes.
Return chicken to skillet and cook for an additional 2 minutes, spooning sauce over chicken.
Taste and adjust seasoning with salt and pepper as needed.
Garnish with chopped fresh parsley and serve immediately with lemon slices.