Melt butter with flour in saucepan over medium heat. Add nutmeg, salt and pepper. Add milk slowly while stirring mixture with a wooden spoon. Bring sauce to boil and cook 10 minutes. Set white sauce aside until it's time to assemble the lasagne.
Brown ground beef in a large sauce pan over high heat with vegetable oil, onion and garlic. Add tomatoes and water just enough to cook a thick meat sauce. Set meat sauce aside until it's time to assemble the lasagne.
Preheat oven to 350°F Bring four quarts of water to a boil. Stir in salt then add noodles four at a time and cook uncovered until tender but firm. Use a large fork or slotted spoon to remove cooked noodles directly to the baking dish.
Spoon meat sauce into baking dish. Make four layers of noodles, as follows: Put first layer of noodles on top of meat sauce. Then alternate each layer with meat sauce, mozzarella and ham. In one of the layers put only white sauce with ham. Cover lasagne with sauce, grated parmesan and a sprinkle of oregano. Bake for 20 minutes. Cover with foil during baking to avoid cheese from burning.