Cut chicken in half crosswise and sprinkle with ¼ teaspoon each salt and pepper.
Place flour on a plate and dredge both sides of the chicken in it. Shake off any excess.
Whisk tomato paste and ⅓ cup water in a small bowl and place near the stove.
Heat 2 tablespoons oil in a large skillet over medium heat.
Add the chicken and cook, turning once, until browned on both sides, about 10 minutes. Transfer to a plate.
Add sopressata to the pan and cook, stirring, until browned, 1 to 2 minutes. Stir in the tomato paste mixture and lemon.
Return the chicken to the pan, cover and cook, turning once, until the sauce has thickened and an instant-read thermometer inserted into the thickest part of the chicken registers 165°F, 5 to 7 minutes.