Reserve some of the fennel leaves to garnish the soup. Chop enough of the fennel bulbs to measure 2 cups.
In a Dutch oven, heat olive oil over medium heat. Add garlic; cook and stir for 1 minute. Add onion; cook until golden brown, stirring occasionally. Add the 2 cups fennel and the carrot; cook until tender, stirring occasionally. Add the water, lentils, salt, and pepper. Bring to boiling; reduce heat. Simmer, uncovered, for 25 to 30 minutes or until lentils are tender.
Meanwhile, in a large skillet, cook sausage until browned. Using a slotted spoon, transfer sausage to lentil mixture. Stir in vinegar. Garnish with the reserved fennel leaves. Makes 10 servings.