Peel and halve the jerusalem artichokes.
In a large pan, heat butter and 2 tablespoons olive oil. Add the onion and fry 2 minutes.
Add jerusalem artichokes, white wine, bay leaf and water to cover. Bring to boil, and cook on low heat until the jerusalem artichokes soften, about 1 hour.
Meanwhile, thinly slice a small lemon (don''t peel).
Add the mushrooms to the pan, then the thyme, lemon slices and 3 tablespoons olive oil, and cook another 20 minutes. Serve warm.