Place the cashews in a bowl and cover with filtered water. Let soak for at least 2 hours or up to 24 hours. Drain and set aside.
Bring a large pot of heavily salted water to a boil and cook the lasagna noodles according to the package directions. Drain, rinse with hot water, and drain again. Drizzle with 1 tablespoon olive oil and gently stir to coat the noodles. Set aside.
In a large skillet heat 2 tablespoons olive oil over medium-high heat. Add the onions, eggplants, mushrooms, and red peppers. Cook the vegetables, stirring occasionally, until they soften, brown, and any juices that the vegetables have released are cooked off, about 15 minutes. Add 2 garlic cloves and cook for 30 seconds. Lower the heat to medium, add the tomatoes, including the juice, 1 teaspoon salt, black pepper, the red pepper flakes, dried basil and oregano and cook until most of the tomato liquid has reduced and the mixture is thick and cooked through, about 20 minutes.
Preheat oven to 350 degrees.
Place the soaked cashews in a blender with about 1/3 cup water, the remaining 2 garlic cloves, lemon juice, and the nutritional yeast. Blend until smooth, scraping down the sides of the blender as needed. If needed, add more water, a little at a time. Remove half the mixture and reserve. To the remaining cashew cheese add the fresh basil and remaining ¼ cup of olive oil and blend until smooth.
Ladle a little of the liquid from the tomato vegetable mixture on the bottom of a 9 by 12 inch baking dish then layer in half the lasagna noodles. Add half of the remaining tomato vegetable mixture and top with the basil cashew cheese. Layer on the remaining lasagna noodles, the rest of the tomato vegetable mixture and then drizzle the top with the reserved cashew cheese. Bake uncovered until hot and bubbly, 30 - 40 minutes. Let cool for a few minutes and serve.