In a large saucepan heat oil over medium heat. Add fennel, yellow onion, and garlic; cook for 5 to 6 minutes or until fennel and onion are tender, stirring occasionally. Add broth, potatoes, milk, and thyme. Bring to boiling; reduce heat. Simmer, covered, for 10 to 15 minutes or until potatoes are tender. Cool slightly.
Meanwhile, in a medium nonstick skillet cook sausage over medium heat until brown, using a wooden spoon to break up sausage as it cooks. Drain off fat.
Transfer potato mixture, half at a time, to a food processor or blender. Cover and process or blend until smooth. Return pureed mixture to saucepan. Stir in sausage and lemon juice; heat through.
Ladle soup into serving bowls. If desired, sprinkle with green onions.