Heat 1 tablespoon oil in a Dutch oven over medium-high heat. Cook and stir 1/2 the lamb cubes in hot oil until browned on all sides, about 5 minutes. Transfer browned meat with a slotted spoon to a plate, reserving drippings in the pot. Add remaining 1 tablespoon oil to the Dutch oven. Cook and stir second 1/2 the lamb cubes until browned on all sides, about 5 minutes. Transfer lamb to plate. Reduce heat to medium-low.
Cook and stir onion, carrots, and garlic in Dutch oven until slightly softened, 3 to 5 minutes. Stir lamb cubes and any accumulated juices, tomatoes, beef stock, thyme, and rosemary into onion mixture and bring to a boil while scraping the browned bits of food off of the bottom of the pan with a wooden spoon. Cover Dutch oven with an oven-proof lid.
Cook stew in the covered Dutch oven in the preheated oven until the lamb is tender, 2 to 3 hours. Stir butternut squash cubes into stew, recover the Dutch oven, and return to the preheated oven until squash is tender, 20 to 25 minutes.