Heat oil in a large pot over medium heat. Add carrots, tomato, onion and garlic; cook, stirring occasionally, until the tomato has broken down and is starting to stick to the bottom of the pan, 4 to 5 minutes. Stir in tomato paste, cumin, salt and pepper; cook, stirring frequently, until the tomato paste is browned, 1 to 2 minutes. Add lentils and water; bring to a boil over high heat. Reduce heat to maintain a simmer and cook, stirring occasionally, until the lentils are soft and the soup is thickened, about 25 minutes.