Heat oil in a large soup pot over medium heat. Add carrots, onions, and celery, and cook until the vegetables begin to soften, 5 to 6 minutes.
Add the mushrooms and garlic, and cook until the mushrooms begin to release their liquid, about 3 minutes.
Add tomatoes (with juice), thyme, water, salt, pepper, and lentils. Bring to a boil over high heat, then reduce to medium-low, cover, and simmer until the lentils are tender, about 35 minutes. Stir in the balsamic vinegar.
Tip: For the best-tasting lentils, look for green French Le Puy lentils or black “beluga” lentils. They’re smaller than plain brown lentils and have a more complex flavor.