Season chicken cutlets with salt and pepper, then dredge in flour, tapping off excess.
In a large skillet, heat olive oil and 2 tablespoons of butter over medium-high heat.
Sauté chicken for 3 to 5 minutes per side until golden brown and the internal temperature reaches 165°F (74°C). Remove chicken and tent with foil.
Deglaze the skillet with white wine, scraping the bottom to release fond. Simmer until liquid is reduced by half.
Add chicken stock and lemon juice. Simmer for 5 minutes until the sauce thickens slightly.
Reduce heat to low and whisk in the remaining 2 tablespoons of cold butter until the sauce is glossy and emulsified.
Return the chicken to the skillet, add lemon slices, and garnish with fresh parsley before serving.