In a small saucepan bring water to a boil and remove pan from heat. Stir in porcini. Soak porcini 20 minutes. Lift out porcini, squeezing out excess liquid, and reserve soaking liquid. In a sieve rinse porcini to remove any grit and pat dry. Chop porcini and transfer to a large bowl. Simmer reserved soaking liquid until reduced to about 1/4 cup.
Pour liquid through a sieve lined with a dampened paper towel into bowl with porcini.
Quarter white mushrooms and in a food processor pulse in 3 batches until finely chopped.
Cut zucchini into 1/4-inch dice. Chop onion and mince garlic. In a 12-inch heavy skillet heat 1 tablespoon butter over moderate heat until foam subsides and cook one third white mushrooms with 2 tablespoons Sherry, stirring, until liquid mushrooms give off is evaporated and they begin to brown.
Add mushroom mixture to porcini. Cook remaining mushrooms in 2 batches in butter with remaining Sherry in same manner and add to porcini mixture. In skillet cook zucchini in 1 tablespoon butter until tender and stir into porcini mixture. In skillet cook onion in remaining tablespoon butter, stirring, until softened. Stir in garlic, thyme, salt, and pepper and cook, stirring, until fragrant, about 30 seconds. Stir onion into mushroom mixture until combined. Filling may be made 1 day ahead and chilled, covered.
In a 3-quart heavy saucepan melt butter over moderately low heat and whisk in flour. Cook roux, whisking, 3 minutes and whisk in milk. Bring sauce to a boil, whisking constantly, and simmer, whisking occasionally, 3 minutes. Stir in Parmesan, mustard, and salt.
Remove pan from heat and cover surface of sauce with wax paper. Sauce may be made 1 day ahead and chilled, covered. Bring sauce to room temperature before proceeding.
Preheat oven to 375°F. and butter a 13 x 9-inch (3-quart) baking dish.
Spread 1 1/4 cups sauce in baking dish and cover with 3 pasta sheets, making sure they don't touch each other.
Spread one third filling over pasta sheets in dish and top with 3 more pasta sheets, gently pressing down layers to remove air pockets. Top pasta sheets with one third mozzarella. Continue layering in same manner with sauce, pasta sheets, filling, and mozzarella, ending with mozzarella (dish will be filled to rim).
Spread remaining sauce over top and sprinkle with Parmesan. On a foil-lined large baking sheet bake lasagne in middle of oven until bubbling and golden, about 45 minutes.
Let lasagne stand 20 minutes. Lasagne may be made 1 day ahead and chilled, covered. Bring lasagne to room temperature and reheat before serving.
