For the white sauce: In a small saucepan melt the butter, stir in flour until smooth. Slowly add milk while stirring, until sauce comes to a low boil and has thickened. Season with salt, pepper and nutmeg. Set aside.
For the squash filling: In a bowl, combine winter squash, sage, thyme, salt and pepper.
For the ricotta filling: In a bowl mix together ricotta cheese, eggs, 1 cup of the Parmesan cheese, mozzarella cheese, sage and nutmeg. Spread half the white sauce in the bottom of a 9X12 inch greased baking dish. Lay 2 lasagna sheets over the sauce, spread with half the squash mixture. Add another layer of lasagna sheets, and then spread with half the ricotta. Repeat process. Top ricotta filling with remaining white sauce and extra Parmesan cheese. Cover the baking pan with foil. Bake for 35 minutes. Uncover and bake another 15 minutes or until golden. Let rest for 10 minutes before serving.
Brown some butter with sage and walnuts and pour over lasagna before serving.