Make bechamel: Heat milk just until small bubbles form around edges. In a saucepan over moderately low heat melt butter, add flour and whisk mixture over moderately low heat for 2 minutes. Slowly stir in milk and bring to a simmer, whisking constantly for 5 minutes. Season with nutmeg, salt and pepper.
Make filling: In a large skillet heat 1 tablespoon each of butter and olive oil over moderate heat , add onions and garlic and cook, stirring occasionally, 20 minutes or until golden brown; season to taste with salt and pepper.
Preheat oven to 450 degrees. Brush zucchini with olive oil, fresh oregano, salt and pepper to taste and arrange on oiled baking sheets. Roast 20 minutes, until soft.
In a large pot of boiling, salted water cook noodles for 3 minutes, or until soft. Drain and pat dry.
Assemble lasagna: Reduce oven temperature to 375 degrees F. In a well-buttered 9-inch square baking dish, spread 1/4 cup bechamel sauce. Top with a lasagna noodle. Spread with another 1/4 cup bechamel. Layer on one-third each of onion mixture, zucchini slices and mozzarella. Top with 1/4 cup bechamel, 1/4 cup Parmesan and a lasagna noodle. Repeat to make 2 more layers, finishing with bechamel and Parmesan. Dot with remaining butter. Cover loosely with foil and bake 10 minutes. Uncover and bake 20 minutes more, or until top is golden and filling is bubbling. Let stand 5 minutes before serving.