In a frying pan over a medium heat, warm a little oil then add the onions, mushrooms and beef and cook and stir until mince is browned. Add the tomatoes, garlic, oregano, basil and bay leaves. Season, stir well and leave to simmer on a low heat for 45 to 50 minutes. Remove and discard the bay leaves once the time is up.
To make the béchamel sauce, melt the butter in a saucepan over a medium heat then add the flour and cook and stir until it forms a golden paste. Gradually whisk in the milk until the sauce thickens. Remove the saucepan from the heat the stir in the cheese, reserving some for the top the lasagne.
Into a baking dish spoon a third of the beef mixture over the base, followed by a layer of lasagne sheets and topped with béchamel sauce. Repeat until the mixture is used up. Top with the reserved grated cheese.
Pop the lasagne under the grill for 10 minutes until cheese has melted.