Butterfly cut the chicken breasts. Then pound with a 2-cup glass measuring cup until 1/4-inch thick.
In a large frying pan, melt 2 tablespoons of the butter over medium heat. Add chicken and saute, turning once, until lightly browned, about 2 minutes on each side. Remove and set aside.
Melt remaining butter in pan. Add shallots and mushrooms. Cook until mushrooms are lightly browned, 3 to 5 minutes. Add Marsala and bring to a boil, scraping up any browned bits from the bottom of the pan. Add cream and lemon juice and return to a boil. Season with salt and pepper to taste.
Return chicken to pan and cook, turning in sauce, for about 3 minutes to reheat and finish cooking.
Serve with buttered fettuccini, rice, or bread.