Heat the olive oil in a large, high-sided frying pan on a medium setting. Add the onion and pepper, and fry until softened, about 6 to 8 minutes. Then, add the garlic, and fry for another minute.
Add the grated carrot, lentils, chopped tomatoes, tomato purée, Worcestershire sauce, and vegetable broth. Season with salt and pepper to taste, stir well, and leave to simmer for 30 minutes.
While the lentil mixture simmers, prepare the white sauce. Melt the vegan butter in a saucepan, then gradually add the flour, constantly stirring until a thick paste has formed.
Gradually pour in the milk, whisking as you go. Simmer and whisk, until all of the milk has been added, and you have a thick sauce. Add the nutritional yeast and some salt to taste, and whisk until smooth.
Preheat the oven to 350 F.
To assemble the lasagna, spread about ⅓ of the ragu in the bottom of a large baking dish. Then, place lasagna sheets on top to cover. Next, spoon over some white sauce, and spread it out in an even layer over the lasagna sheets. Repeat this process 2 more times, layering ragu, lasagna sheets, then white sauce.
Sprinkle the vegan cheese all over the top of the final white sauce layer. Bake the lasagna for 40 minutes. Serve with fresh chopped parsley on top if desired.