Preheat the oven to 400°F (200°C).
Soak 1/2 cup cashews in hot water for 5 minutes, then drain; alternatively simmer them for 5 minutes, then drain.
Peel and finely chop the onion. Heat a little olive oil in a non-stick frying pan and cook the onion until glossy, about 4–5 minutes.
Add 2 cloves chopped garlic to the pan and cook 1–2 minutes until fragrant.
Stir in 14 oz chopped tomatoes, 5 oz tomato puree, 1 tsp paprika, 2 tsp oregano, 2 tsp basil, and salt and pepper to taste; simmer the sauce for about 5 minutes.
Add 1.5 cups brown lentils (canned or cooked) to the tomato sauce and cook 1–2 minutes to warm through; remove from heat.
Make the white (cashew) sauce: combine the drained soaked cashews, 1/2 cup dairy-free milk, 1 clove whole garlic, 1 Tbsp nutritional yeast, 1/2 tsp nutmeg (optional), and salt and pepper to taste in a blender or use an immersion blender until completely smooth and creamy.
Spoon a thin layer of the lentil bolognese into the bottom of the oven-safe dish to prevent sticking.
Assemble the lasagna in layers: place pasta sheets, then lentil bolognese, then cashew white sauce. Repeat layers to fill the dish—the recipe filled our 9 x 7 x 3 in dish with about 6 pasta layers, ending with a final layer of white sauce.
Sprinkle the top with 7 oz dairy-free grated cheese or vegan parmesan (or extra nutritional yeast).
Bake in the preheated oven for 30 minutes until hot and set, then remove and let rest a few minutes before slicing.