In a saucepan, heat 1 tablespoon of the oil over moderate heat. Sauté the onions and garlic for about 5 minutes until soft. Add the tomatoes with their juices, the tomato purée and herbs. Simmer, stirring occasionally, for 15 minutes until thickened.
Meanwhile, in a non-stick frying pan, heat the remaining oil over moderate heat and sauté the courgettes, carrots and celery, stirring frequently, for 7 minutes or until slightly soft.
Bring a large pan of water to the boil. Add the lasagne noodles and cook according to packet instructions. Drain. In a small bowl, combine the ricotta, egg white and parsley.
Preheat the oven to 180°C (350°F, gas mark 4). Spread a quarter of the tomato sauce over the bottom of a 33x23x5cm (13x9x2in) baking dish. Arrange a third of the lasagne over it in an even layer. Spread half the ricotta mixture over the pasta and scatter half the vegetables on top.
Repeat the layers, then add another layer of sauce and the last of the lasagne. Spread the remaining sauce on top and scatter over the mozzarella and Parmesan. Bake for about 45 minutes or until browned around the edges.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.