Preheat oven to 400 degrees F (205 degrees C).

Pour olive oil in an 8x8-inch glass baking dish. Place the chicken breasts in the dish, coating each side with oil. Squeeze the juice of 1/2 lemon over each chicken breast. Slice the rest of the lemon and place a lemon slice on top of each chicken piece.

Bake in the preheated oven until no longer pink in the center and the juices run clear, 30 to 40 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).

Melt butter in a skillet over medium heat; add mushrooms. Cook and stir until mushrooms are brown and liquid is evaporated, about 6 minutes. Sprinkle flour over mushrooms and stir until coated. Add chicken broth, stirring to make a medium-thick sauce. Allow sauce to reduce, adjusting with a little more broth to make a creamy sauce. Add fresh parsley at the last minute. Spoon the sauce over the baked chicken breasts.