Cook lasagne in boiling salted water in a large pot until al dente. Drain.
Meanwhile heat one half tablespoon of olive oil in a casserole dish over medium heat. Add the chopped onion, celery and carrots, stir and cook until onions have softened. Add mushrooms and garlic and continue to cook until the mushrooms have released their liquid, 2 or 3 minutes. Add wine and cook until most of the liquid has evaporated. Stir in chopped tomatoes (include liquid), sun-dried tomatoes and thyme. Bring to a simmer then reduce heat to low and simmer until thick. Season with salt and pepper.
To make the white sauce heat remaining oil in a heavy pan over low heat. Add flour and whisk constantly until the flour begins to turn a light brown. Remove pan from heat and whisk in cream. Season with nutmeg and a pinch of salt. Remove from heat and set aside.
To assemble, spread 1/2 cup of the mushroom sauce in the bottom of a casserole dish, add one layer of pasta, then another 1/2 cup of mushroom sauce. Arrange a single layer of the fresh spinach leaves over the sauce and drizzle them with 1/3 cup of the white sauce. Sprinkle 2 tablespoons of the grated Parmesan cheese over the spinach and top with another layer of the pasta. Repeat 5 times.
In a preheated 190 degrees C oven bake for 40 minutes. Let stand for 10 to 15 minutes. Serve warm.