Peel and chop the onion and slice mozzarella thinly. Heat oil and fry onion and mince for 5 minutes, sirring. Add sauce, cover and simmer for 20 minutes. Season.
Meanwhile, melt butter in a pan. Stir in the flour and cook for 1 minute. Remove from heat and add milk. Stir the sauce over a low heat until thickened.
Spread a third of the meat sauce over the base of a 2 litre dish. Top with a third of the mozzarella, cover with a third of the lasagne sheets. Repeat layers twice. Spoon over white sauce. Sprinkle with Parmesan.