Preheat oven to 180 C / Gas 4. Pour 4 tablespoons of pasta sauce onto the bottom of a large oven-proof baking dish.
Heat vegetable oil in a large frying pan over medium heat; cook and stir the sausage and courgette until cooked, 10 to 12 minutes. While the sausage and courgettes are cooking, mix together the ricotta cheese, egg white, mozzarella cheese, and 4 tablespoons of the Parmesan cheese in a bowl until well combined.
Place 3 lasagne sheets on top of the pasta sauce in the baking dish, overlapping if necessary. Spread half the sausage-courgette mixture on top. Spread half the cheese mixture over the sausage-courgette mixture, and pour 1 tomato pasta sauce evenly over the cheese mixture. Spread the sauce over the cheese mixture with a spoon or spatula. Repeat layers, then sprinkle the top with remaining Parmesan cheese.
Bake in the oven until the lasagne is bubbling and the cheese has browned, about 45 minutes.