Adjust oven rack to middle position and heat oven to 200 degrees. Halve chicken horizontally, then cover chicken halves with plastic wrap and pound to an even ¼ inch thickness with meat pounder. Place flour in a shallow dish or pie plate.

Pat chicken dry with paper towels and season with salt and pepper. Working with 1 cutlet at a time, dredge in flour mixture, shaking off excess, and transfer to large plate.

Heat 2 tbs oil in a 12 inch skillet over medium-high heat until shimmering. Place 4 cutlets in skillet and cook until golden brown on first side, about 3 minutes. Flip cutlets, reduce heat to medium, and cook until no longer pink and lightly browned on second side, about 2 minutes longer; transfer to large oven safe plate. Wipe out skillet. Repeat with remaining 2 tbs oil and remaining cutlets. Tent loosely with aluminum foil and transfer to oven to keep warm while making sauce.

Cook pancetta in now-empty skillet over low heat, stirring occasionally and scraping up any browned bits, until crisp, about 5 minutes; remove pancetta with slotted spoon and transfer to paper towel lined plate. Add mushrooms to skillet, increase heat to medium-high and cook stirring occasionally, until softened and lightly browned, about 8 minutes. Stir in garlic and tomato paste, and crisp pancetta and cook until tomato paste begins to brown, about 1 minute. Off heat stir in Marsala, scraping any browned bits. Return to high heat, bring to a vigorous simmer, and cook stirring occasionally, until sauce is thickened and measures 1 ¼ cups, about 5 minutes. Off heat, stir in lemon juice and any accumulated chicken juices. Whisk in butter, 1 piece at a time. Stir in parsley and season with salt and pepper to taste. Pour sauce over chicken and serve immediately.