Heat oven to 325F degrees with the oven rack adjusted to the middle.
PREPARE THE CHICKEN BREASTS
Cut the chicken breasts in half horizontally to make four pieces. Cover the chicken in wax paper or plastic wrap, and lightly pound the breasts out evenly, about ½ inch thickness. (You can do this with with a meat pounder or the bottom of a flat jar or (heavy) glass.) Pat the chicken dry with a paper towel and season each slice with the salt and pepper. Place the flour on a plate, and dip each chicken breast in the flour, shaking off any excess, then transfer each piece to a separate plate.
Heat 3 tablespoons oil in a 12 inch non-stick skillet over medium-high heat. Place two chicken pieces in the skillet and cook until golden brown on one side, 3-4 minutes. Turn the chicken over, and continue cooking for 3-6 more minutes, until the chicken is no longer pink inside. Wipe out the skillet, and repeat with the remaining oil and the other two pieces of chicken. Place all four pieces of chicken on a heatproof platter or pie plate, tented loosely with aluminum foil, and bake in the low warm oven while you make the mushroom sauce.
To make the mushroom sauce, add the cut pieces of bacon into the same skillet you cooked the chicken, turn it up to medium-high heat, then cook the bacon stirring and scraping the pan bits with a wooden spoon until it's crisp, about 5 minutes. Remove bacon and transfer to a paper-towel lined plate.
Add the shallots to the empty pan and cook on medium heat until soft, stirring occasionally with a wooden spoon, about 3-4 minutes.
Add the sliced mushrooms to the pan and continue cooking on medium heat stirring occasionally, until mushrooms are soft and lightly browned on the edges, 6-8 minutes. Stir in the minced garlic clove, tomato paste and the cooked bacon, continue cooking for one minute, then remove the pan from the heat.
Stir in the Marsala wine, scraping up any bits from the bottom of the pan with your wooden spoon. Return to the heat, increase heat to medium high, and cook the mixture for about 5 minutes, or until the sauce is slightly thickened, stirring it occasionally.
Turn off heat and stir in the lemon juice and butter, a pinch of salt and pepper, and one tablespoon of fresh parsley. Stir gently to combine together.
Remove chicken from the oven and place on a serving platter, pour warm sauce over the chicken and sprinkle with remaining fresh parsley and serve immediately.