Fry onion, garlic and celery in olive oil for a couple of minutes. Add mushrooms. Pick thyme leaves and fold it in along with crushed tomatoes. Let everything simmer for 5 to 10 minutes. Season with salt, pepper and sugar. Set aside to cool.
Sauce:
Melt butter in saucepan over medium heat and whisk in flour until it comes together. Add milk a little at a time and whisk until sauce thickens. Season with nutmeg, salt and pepper.
Rub eggplant and zucchini slices with olive oil. Fry in pan, sprinkle with salt and set aside.
Preheat oven to 375°F.
Pour some of the sauce into bottom of baking dish. Place a layer of lasagna sheets on top. Then add slices of eggplant and zucchini and spread vegetable filling on top. Add another layer of sauce. Build layer upon layer until all filling is used up. Top with mozzarella. Bake in lower part of oven for about 30 minutes. Sprinkle over chopped thyme before serving.