Place heatproof plate into a 200° F oven. Heat 12″ heavy bottom skillet to medium high until very hot. Pat chicken breasts dry. Meanwhile, place flour in a ziploc bag; season both side of chicken with salt & pepper. Put chicken in ziploc and coat both sides with flour. Shake off excess flour and set aside. Add oil to hot skillet and heat until shimmering. Place chicken in single layer in skillet and cook until golden brown; about 3 minutes. Using tongs, flip cutlets on second side and cook 3 minutes longer. Transfer chicken to heated plate and return plate to oven.
Return skillet to low heat and add pancetta; saute, stirring occasionally and scraping pan bottom to loosen browned bits until pancetta is brown and crisp, about 4 minutes. With slotted spoon, transfer pancetta to paper towel-lined plate. Add mushrooms and onions and increase heat to medium-high; saute, stirring occasionally and scraping pan bottom, until liquid released by mushrooms evaporated and mushrooms begin to brown, about 8 minutes. Add garlic, tomato paste, and cooked pancetta; saute while stirring until tomato paste begins to brown; about 1 minute. Off heat, add Marsala; return pan to high heat and simmer vigorously, scraping browned bits from pan bottom, until sauce is syrupy and reduced to about 1-1/4 cups, about 5 minutes. Off heat, add lemon juice and any accumulated juices from chicken; whisk in butter 1 tablespoon at a time. Season to taste with salt and pepper, and stir in parsley. Pour sauce over chicken and serve immediately.