Combine all the ingredients in a high-speed blender. Blend until silky smooth, adding a splash of water if necessary to help blend. Season with salt and pepper. This step can be done in advance and stored in the fridge.
Preheat the oven to 375°. Slice squash in half lengthwise and scoop out seeds and stringy bits. Drizzle flesh with olive oil and place on baking sheet flesh side up. Bake until soft, about 30-40 minutes. Allow to cool.
When cool enough to handle, peel the skin off the squash. Place flesh in a high-speed blender and blend until very smooth. If necessary add a few splashes of water to help blend. Measure out 2 cups for recipe use. Season with salt and pepper. This step can be done in advance and stored in the fridge.
In a large skillet, heat olive oil over medium high heat. Add the kale in batches, adding more to the pan as the kale wilts. Add the chopped garlic and cook for a few minutes more. Remove from heat and stir in the lemon juice, red chili flakes, and season with salt and pepper
Preheat oven to 350°F and lightly grease baking pan with olive oil.
Cook the noodles according to package instructions. Drain and toss with a little bit of olive oil to prevent them from sticking to one another.
Line the bottom of the lasagna pan with noodles (about 3 sheets). Layer with half of the butternut squash puree, then top with 1/2 of the kale, and 1/3 of the béchamel. Add another layer of noodles, and top with remaining butternut squash, all but a 1/4 cup of the kale, and another 1/3 of béchamel. Add the last layer of of noodles and then the remaining kale, béchamel, and scatter vegan cheese on top.
Bake in oven until heated through and bubbling, about 40-45 minutes