In a Dutch oven or large soup pot heat 1 tablespoon of the oil over medium-high heat and sauté the onion, until beginning to brown, about 5 minutes. Add carrots and celery and cook, stirring, until soft, about 5 minutes. Add lentils, chicken stock, and water and bring to a boil. Reduce the heat, cover and simmer until the lentils are tender, about 30 minutes.
When the lentils are just about tender, heat the remaining tablespoon of oil in a sauté pan over medium heat and brown sausage on all sides. Transfer to a cutting board and cut into 1/2-inch slices. Stir the sausage into the soup. Stir in the vinegar and season to taste with salt and pepper.