Reserve fennel tops for garnish. Chop enough of the fennel bulb to equal 1 cup. Set aside.
In a Dutch oven, cook garlic in hot oil over medium heat for 1 minute. Add onion and cook until tender and golden brown. Add carrots and chopped fennel; cook until tender, stirring occasionally. Add water, lentils, salt, and pepper. Bring to boiling; reduce heat. Simmer, uncovered, for 25 to 30 minutes or until vegetables are tender.
Meanwhile, in a large skillet brown sausage on all sides over medium heat. Using a slotted spoon, transfer sausage to soup. Stir in vinegar. Ladle into bowls. Garnish with fennel tops. Makes 5 to 6 servings.