In a large skillet, heat the olive oil and butter over medium-high heat.
Season the pork chops with salt and pepper. On a plate, place the flour and then zest the lemon over the flour and place the lemon aside. Coat each pork chop with the flour-zest mixture on both sides and place into the hot skillet and cover with a splatter screen. Cook for about 2-3 minutes depending on thickness. Repeat on the other side and then place the chops on a plate.
Reduce heat to medium-low. Add the mushrooms to the pan and allow to saute for 2 minutes. Add the garlic, saute for 30 seconds.
Increase the heat to medium and add the chicken broth and scrap the bottom of the pan. When the liquid is reduced by about half, add the pork back into the pan. Cut the lemon in half, juice half of the lemon and gently add the juice to the pan. Cut the remaining half of the lemon into slices, toss them into the pan and cook for another minute or so. Serve hot.