Heat the oil in a heavy large pot over medium heat. Add the onion, carrots, and celery. Add the garlic, salt, and pepper and saute until all the vegetables are tender, about 5 to 8 minutes. Add the tomatoes with their juices. Simmer until the juices evaporate a little and the tomatoes break down, stirring occasionally, about 8 minutes. Add the lentils and mix to coat. Add the broth and stir. Add the thyme sprigs. Bring to a boil over high heat. Cover and simmer over low heat until the lentils are almost tender, about 30 minutes.
Stir in the pasta. Simmer until the pasta is tender but still firm to the bite, about 8 minutes. Season with salt and pepper, to taste.
Ladle the soup into bowls. Sprinkle with the Parmesan, drizzle with olive oil, and serve.