Heat the olive oil in a large pot over medium heat. Add the lamb sausage and cook until browned, breaking it up with a spoon as it cooks.
Add the onion, carrots, and garlic to the pot. Stir and cook for 5 minutes until the vegetables soften.
Stir in the lentils, diced tomatoes, vegetable broth, and dried oregano. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 30 minutes until the lentils are tender.
Stir in the olives and season with salt and black pepper. Simmer uncovered for 5 more minutes to let the flavors blend.