Heat a large soup pot over high heat and swirl in the olive oil. Add the onion, carrots, celery, garlic, and 1 teaspoon of the salt. Reduce the heat to low and saute until the vegetables are lightly caramelized, about 5 minutes. Add the tomato and cook for 2 minutes. Stir in the tomato paste and cook for another 2 minutes.
Add the lentils, thyme, bay leaf, pepper, and the remaining 2 teaspoons salt. Add the broth and water, and bring to a boil, skimming and discarding any foam as it rises to the surface. Reduce the heat and simmer until the lentils are tender, 15 to 20 minutes. (The cooking time depends on the age of the dried lentils.) Stir in the vinegar. Season to taste with salt and pepper. If needed, thin the soup with additional water or broth for the desired consistency. Serve in a bowl topped with fresh croutons, if using.