Pat the lamb dry using paper towels and season the meat on all sides with salt and pepper. To remove remaining moisture, lightly dust the lamb with flour, shaking off any excess.
Heat 2 tablespoons of the olive oil in a large heavy bottomed pot or 7-quart Dutch oven over medium-high heat.
Sear the lamb until browned on all sides, 5 to 6 minutes total. Place the seared lamb on a paper towel-lined plate to allow excess fat to drain and set aside.
Return the pan to medium heat, then add the remaining olive oil and heat through. Add the onions, celery, and carrots and cook until the onions become translucent and the vegetables are tender, about 6 minutes.
Add the red wine to deglaze the pan, scraping up any bits of meat from the bottom of the pan using a spoon. Allow the wine to simmer and reduce by about half, for about 10 minutes.
Add the tomatoes with their liquid, thyme, bay leaves, and seared lamb. Cover the pot and simmer on low, stirring occasionally, until the lamb is tender, about 2 hours. Season to taste with salt and pepper.
Bring a large pot of water to the boil; add salt and bring back to the boil. Pour in the pasta and cook, stirring occasionally, until al dente, about 10 minutes. Drain and return the pasta to the pot.
Ladle in the enough of the lamb ragu to coat the pasta, then stir in the crushed red pepper flakes.
Divide the pasta among warmed pasta bowls, topping with extra sauce if desired. Sprinkle with Parmesan and serve.