In a large Dutch oven, over medium heat, add the oil. When the oil is hot, but not smoking add the chops. Sear for 2 to 3 minutes on each side Remove the chops from the pan and set aside. Add the beer and continue to cook for 1 minute, scraping any brown particles off the bottom of the pan.
Add the lamb back to the pan. In a mixing bowl, toss the vegetables with salt and pepper. Add the vegetables to the pan. Cover with the stock Bring the liquid to a boil, cover and reduce the heat to medium low Simmer for about 2 hours or until the lamb falls off the bone.
Stir in the roux and continue to cook for 10 minutes.