To make the meat sauce, lightly spray a large saucepan with olive oil, add the onion and garlic and cook over medium heat, stirring often for 5 minutes until soft. Add tomato paste and cook for 2 minutes.
Increase heat to high, add the mince and cook, stirring with a wooden spoon to break it up for 5 minutes or until the mince changes colour. Stir in the mushrooms, tomatoes, oregano, sugar and water. Season with pepper and bring to the boil.
Reduce heat to medium-low, cover and cook, stirring occasionally, for 20 minutes. Remove the lid and simmer, uncovered, a further 10-15 minutes until sauce has thickened slightly. Taste and season with more pepper if needed.
For the white sauce, melt the margarine spread in a medium saucepan over medium heat. Add the flours and cook, stirring, for 1 minute. Remove the pan from the heat, gradually add the milk, 1/2 cup at a time, whisking constantly until all been added. Return to heat and cook, stirring constantly for about 5 minutes until sauce has thickened. Remove from the heat, stir in the nutmeg.
Preheat oven to 200°C (180°C fan-forced). Lightly grease a 6cm x 18cm x 24cm ovenproof dish with olive oil spray. Spoon about 1/2 cup of the meat sauce over base of greased dish. Cover with a single layer of lasagne sheets, trimming to fit if necessary. Top with half the remaining meat sauce, then drizzle over about 1/3 cup of the white sauce . Top with a layer of lasagne, remaining meat sauce and 1/3 cup of white sauce. Top with a final layer of lasagne then spoon over the remaining white sauce to cover the pasta.
Cover with a sheet baking paper then foil. Place onto a tray and bake for 30 minutes. Remove baking paper and foil, sprinkle over the cheese and bake for a further 15-20 minutes or until the pasta is tender when tested with a skewer.
Cut into pieces and serve with salad or steamed vegetables.