Melt 1 tablespoon of butter and olive oil in a large pan over medium heat.

Mix flour, salt, and pepper in a shallow dish.

Dredge chicken breasts in the flour mixture, ensuring they are evenly coated.

Fry the chicken in the pan in batches, adding butter if the pan gets too dry, until golden brown and cooked through.

Remove chicken to a paper towel-lined plate to drain excess oil.

Pour white wine into the pan and scrape up any browned bits from the bottom to deglaze the pan.

Allow the wine to reduce by half, concentrating the flavor.

Pour in the chicken stock and bring to a simmer.

Halve and juice the lemons, ensuring no seeds fall into the juice.

Add the lemon juice, capers, salt, and pepper to taste to the sauce.

Allow the sauce to simmer for a few minutes, letting the flavors meld together.

Add the remaining tablespoon of butter and allow it to melt into the sauce, enriching its texture.

Serve the chicken immediately, pouring the sauce generously over the top.