Heat the oil over medium heat in a pot. Add the onion, carrot, celery and garlic, and sausage; sauté until the onions start to soften, about 4 minutes. Season with salt and pepper.
Add the broth, tomato, thyme, and lentils. Stir and bring to a simmer. Cover with a lid and simmer until lentils are soft, about 20 minutes. Season with salt and pepper to taste (if the soup is too thick thin it out with a little more broth). Remove the thyme sprigs.
Ladle into bowls, place the cheese on top, and serve with bread. Garnish with celery leaves (allow the cheese to get melty from the heat of the soup before serving if you desire).