Combine 4 cups water, broth, and lentils in a large saucepan over medium heat. Bring to a simmer. Cook 30 minutes or until almost tender.
Heat oil in a saucepan over medium-high heat. Add onion, carrot, rosemary, and garlic to pan. Sauté 10 minutes or until tender. Add sausage; cook 5 minutes, stirring to crumble. Add tomato paste and remaining ingredients; cook for 1 minute or until heated. Add sausage mixture to lentils; bring to a boil. Cook 30 minutes or until lentils are tender.