Whisk first 4 ingredients in medium bowl to blend. Season with salt and pepper.
Cook green beans in large pot of boiling water until crisp-tender, about 5 minutes. Drain. Transfer to large bowl of ice water. Drain beans. Pat dry. (Can be made 1 day ahead. Cover and chill dressing. Wrap green beans in paper towels and chill.)
Place beans in large bowl. Add fennel, mushrooms, parsley, chives and lemon peel. Drizzle dressing over; toss. Season with salt and pepper. Cover and chill 30 minutes. Toss again and serve.