Preheat oven to 375. Trim the ends and any brown spots off the fennel. Chop a handful of the feathery tops and set aside for garnish. Discard the rest. Cut the fennel bulb through the core into 1/2 inch slices. Combine the fennel, potatoes, and garlic in a shallow roasting pan. Drizzle with the olive oil and toss to coat. Roast for 10 minutes. Stir the vegetables and continue roasting until lightly golden and nearly tender when pierced with the tip of a knife, about 10 minutes longer.
In large saucepan, combine the broth and thyme and bring to a boil over high heat. Reduce the heat to low and add the roasted vegetables. Cover and simmer for 5 minutes. Remove from the heat and stir in the lemon juice, salt, and pepper.
Carefully transfer the hot soup in small batches to a blender or food processor. Process until smooth and return each batch to the saucepan. Additional broth can be added if the soup is too thick. Ladle into bowls, garnish with the chopped fennel tops, and serve.