Prepare the lasagna noodles according to instructions on package, reserving 3 cups of cooking liquid.
To make the sauce, place the raw cashews and 1 cup of reserved water in a blender or food processor and process until the sauce is smooth. Add more water as needed until sauce has a creamy, alfredo-like texture, neither too thick nor too thin. Add the lemon juice, garlic, 2 tablespoons of olive oil, nutritional yeast, and rosemary. Process again until smooth. Season with salt and pepper to taste.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the onion and cook until softened, about 5 minutes, stirring occasionally. Add the mushrooms and cook until the liquid evaporates and the mushrooms begin to brown, about 8 minutes. Stir in the kale and continue cooking until wilted, about 2 minutes more; remove from heat.
Spread about ½ cup of the cashew sauce on the bottom of a 8 x 8 inch baking dish that's been lightly coated with oil (I use an oil mister). Layer 4 lasagna noodles and top with half of the veggie mixture. Top with ⅓ of the remaining cashew sauce, 4 more noodles, remaining veggie mixture, another third of the cashew sauce, and then the rest of the noodles. Spread the last of the cashew sauce over the top of the lasagna. Cover with foil and bake for 30 minutes. Let the lasagna rest for 5 minutes, then cut into pieces and serve.