Slice each breast horizontally into two cutlets and pound to an even 1/2-inch thickness. Season with salt and pepper and dredge lightly in flour.
Heat olive oil in a wide skillet over medium-high. Cook the cutlets in two batches for 3 to 4 minutes per side, until the thickest part reaches 165°F; transfer to a plate.
Add broth and lemon juice to the skillet and scrape up the browned bits. Simmer for 3 minutes.
Turn off the heat and whisk in cold butter a piece at a time. Return the chicken for 1 minute, coat with sauce and serve.