Warm oil in a pan over medium-high heat. Sprinkle lamb with salt and cook, turning occasionally, until browned, about 8 minutes. Transfer to slow cooker.
Drain off all but 2 Tbsp. fat from pan. Add onions and carrot; sauté 3 minutes. Pour in wine and bring to a boil, stirring to loosen brown bits at bottom of pan. Transfer mixture to slow cooker. Stir in tomatoes, garlic and rosemary. Cover and cook on low until meat shreds with a fork, 5 to 6 hours. Shred meat and season sauce with salt.
Bring a large pot of salted water to boil. Cook rigatoni until tender, about 10 minutes; drain. Serve rigatoni topped with stew and sprinkle with Parmesan, if desired.