In a 3 qt. saucepan, melt the butter over medium-high heat. Whisk in the flour and cook, whisking continuously for about 2 minutes. Slowly add the milk while continuing to whisk, bring to a simmer over medium-high heat. Reduce the heat to medium and continue to whisk until the sauce has thickened about 5-10 minutes. Add the salt, pepper, and nutmeg. Set aside.
Preheat the oven to 350° F and place the oven rack in the center of the oven.
In a 9-inch X 13-inch baking dish, spread half of the béchamel on the bottom of the dish, and top with a single layer of lasagna noodles, slightly overlapping in order to fit in the bottom.
Scatter half of the mushrooms over the noodles, and top with dollops of the goat cheese mixture. Top with another layer of noodles and spread with half of the remaining béchamel sauce. Spread the tomato and leek mixture evenly over the béchamel sauce.
Cover with a third layer of lasagna noodles and top with dollops of the remaining goat cheese mixture followed by the remaining mushroom mixture.
Cover with the final layer of lasagna noodles and spread the remaining béchamel sauce evenly over the noodles. Sprinkle the remaining 1 cup of mozzarella cheese and 1/2 cup of parmesan cheese on top.
Bake for 50 minutes to one hour or until golden brown on top and bubbling. Let the lasagna rest for 15 minutes before serving.Lasagna can be cooled, covered and refrigerated overnight. To reheat, bring to room temperature, cover with foil, and reheat in a 325°F oven for 25 minutes.