Season both sides of the chicken cutlets with salt and black pepper.
Place flour in a shallow dish and dredge each cutlet, shaking off the excess.
In a large skillet, heat olive oil and 1 tablespoon of butter over medium-high heat until the butter foam subsides.
Working in batches, sear the chicken cutlets for 3 to 4 minutes per side until golden brown and an internal temperature of 165°F (74°C) is reached.
Transfer the cooked chicken to a plate and tent with foil to keep warm.
Reduce the heat to medium and add the minced garlic to the skillet, sautéing for 1 minute until fragrant.
Deglaze the pan with chicken stock and lemon juice, scraping the bottom with a wooden spoon to release any browned bits.
Simmer the liquid for 3 to 5 minutes until reduced by approximately half.
Whisk in the remaining 3 tablespoons of butter until a smooth, emulsified sauce forms.
Add the lemon slices to the sauce and return the chicken to the skillet.
Spoon the sauce over the cutlets, garnish with chopped parsley, and serve immediately.