Place a large skillet over medium-high heat and sauté garlic and onion in olive oil until translucent.
Add pumpkin, thyme and mushrooms and cook until they have released most of their liquid, stirring frequently.
Now, stir in the baby spinach and soy milk. Season with salt and pepper to taste, then remove from heat.
Preheat the oven to 350 °F (180 °C) and prepare a casserole dish.
Make the white sauce by adding all ingredients to a blender. Blend until smooth, adjust to taste preferences, then set aside.
Layer the lasagna by alternating between the veggies, white sauce and lasagna sheets. Finish with a layer of white sauce, then sprinkle with additional vegan cheese shreds or mozzarella if wanted.
Cover the dish with a lid or foil and place it on the middle rack in the oven for 40 minutes.
You can remove the lid for the last 10 minutes to let the top brown!
Remove the lasagna from the oven and allow it to cool for a few minutes before serving.