In a large skillet over medium heat, add ground lamb and start to brown. Once little pink remains, add in carrots, celery and onions; cook until the vegetables just start to soften and the meat is fully browned.
Add garlic and cook until fragrant, about 1 minute. Add the red wine and scrape up any brown bits on the bottom, deglazing the pan. Cook for about 5 minutes to cook down the wine.
Add in tomatoes and break apart in the pan. Add in thyme, tomato paste and 2 cups water. Mix together until combined and cover the pot with a lid. Simmer on low heat until the mixture has cooked down and is thick. Add in remaining 2 cups water, repeat process. This in total should take around 2-3 hours.
Add in milk and red pepper flakes and cook for 30 minutes to allow flavors to deepen. Serve over hot cooked pasta.