Heat oil in a large skillet over medium heat. Cook onion, celery, carrots, and garlic with salt, stirring occasionally, until limp and browning, about 10 minutes. Transfer vegetables to a slow cooker with tomato sauce, lentils, water, broth, bay leaf, thyme, and vinegar. Cook on Low for 6 hours.
For vinaigrette, whisk together olive oil, vinegar, garlic, and salt.
Taste soup for salt, then serve with a drizzle of vinaigrette over each bowl.