Preheat oven to 400°
Season the lamb chops generously with salt, pepper and thyme.
In a large cast iron skillet or a straight sided skillet than can transfer to the oven, heat olive oil over high heat. Once the oil is shimmering, not smoking, add the chops. Cook for 2 minutes per side, including the edges.
Once all the sides have been seared and are a gorgeous caramel color turn the heat off. Add the mushrooms, garlic cloves and 2 Tablespoons of butter. Place skillet into preheated oven for 5 minutes for medium rare.
Remove the skillet from the oven and place on the stove (be very careful it is very hot and your first instinct is to grab the handle when a skillet is on the stove-cover the handle with an oven mit).
Remove the chops to a plate and set aside. Add the water, lemon juice, red pepper flakes, remaining butter or more if you like and parsley. Scrape up the brown bits on the bottom of the pan. Once the butter is melted turn the heat on to medium high. Allow the sauce to thicken slightly. Add back the chops and spoon the sauce over top.
Serve hot with pan sauce.
**If you can only find lamb chops all you need to do is omit the oven step. Since lamb chops are typically thinner you just need to sear in them the hot pan for 3 minutes a side for medium-rare. Once they are cooked remove to a plate and set aside. Add the mushrooms, garlic and butter to pan and let saute for 5-7 minutes until the mushrooms soften and the garlic becomes soft. Then follow instructions for pan sauce.