Preheat oven to 180 degrees C. Pour 1/4 cup of spaghetti sauce into the bottom of a 20x30cm baking dish.
Heat vegetable oil in a large frypan over medium heat; cook and stir the mince and zucchini until the meat is no longer pink and the zucchini pieces are tender, 10 to 12 minutes. Drain excess fat from the frypan and set the mixture aside. While the mince and zucchinis are cooking, mix together the ricotta cheese, egg white, mozzarella cheese and 1/4 cup of Parmesan cheese in a bowl until well combined.
Place 3 sheets lasagne into the bottom of the baking dish on top of the spaghetti sauce, overlapping slightly if necessary. Spread half the mince-zucchini mixture on top of the lasagne. Spread half the cheese mixture over the meat and zucchini, and pour 1 cup of spaghetti sauce evenly over the cheese mixture. Spread the sauce over the cheese mixture with a spoon or spatula. Repeat layers, starting with 3 more sheets of lasagne, the rest of the mince mixture, the rest of the cheese mixture and 1 more cup of spaghetti sauce. Sprinkle the top with 1/2 cup of Parmesan cheese.
Bake in the preheated oven until the lasagne is bubbling and the Parmesan cheese has browned, about 45 minutes.