In a pot, heat olive oil over medium heat. Add onion, garlic, and celery; cook, stirring, until tender, 6 to 8 minutes.
Increase heat to high and add tomatoes; cook for 1 minute. Add lentils, turnip, and 6 cups water.
Bring to a boil, then reduce heat and simmer until lentils are tender, 20 to 25 minutes. Stir in parsley and vinegar. Season with salt and pepper.