Heat oil in a large Dutch oven over medium heat until hot but not smoking; add chops. Sear on each side, 2 to 3 minutes. Remove from the pan and set aside.
Pour beer into the pot and cook for 1 minute, scraping up any browned bits from the bottom of the pan with a wooden spoon. Add lamb back to the pot.
Toss potatoes, carrots, and onions with salt and pepper in a mixing bowl and add to the pot. Cover with lamb stock and bring to a boil. Cover and reduce heat to medium-low. Simmer until lamb falls off the bone, about 2 hours. Stir in roux and continue to cook for 10 minutes. Stir in parsley and spoon into serving bowls.