Preheat oven to 375ºF. Place a large pot of water over high heat to cook the pasta. When the water is boiling, add some salt and drop the pasta. Cook to al dente according to package directions. Drain the pasta and reserve.
Place a medium pot over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Add the ground lamb to the pot and cook until golden brown, 5-6 minutes.
Add the onion, garlic, carrot, thyme, cinnamon and allspice to the pot, season with salt and pepper, and cook until the veggies are tender, 4-5 minutes.
Add the can of tomatoes to the pot and gently break them up with a potato masher or back of a wooden spoon. Simmer the sauce until lightly thickened, 4-5 minutes.