Preheat the oven to 375°F (190°C).
Make the vegan ricotta according to your recipe or prepare it ahead and keep refrigerated until assembling.
Dice the mushrooms and zucchini.
In a large skillet over medium-high heat, sauté the mushrooms for about 3 minutes using 1–3 tablespoons water or vegetable broth for an oil-free method; add more liquid as needed.
Add the diced zucchini to the skillet and sauté for about 5 minutes until tender.
Add the baby spinach and cook, stirring, about 1 minute until just wilted. Remove the pan from heat and set the vegetables aside.
Spoon 1.5 cups marinara sauce into the bottom of a deep 9 x 13-inch casserole dish and spread into an even layer.
Place 4 no-boil lasagna noodles over the sauce. Dollop half of the vegan ricotta evenly over the noodles, then spread half of the sautéed vegetables, and pour 1.5 cups marinara over the layer.
Add 4 more noodles, spread the remaining ricotta in dollops, add the remaining vegetables, and pour another 1.5 cups marinara.
Top with the final 4 noodles and finish with the last 1.5 cups marinara, ensuring the noodles are well covered with sauce.
Cover the dish tightly with foil and bake for 45 minutes. Remove the foil and bake uncovered for an additional 10–15 minutes until heated through and edges bubble.
Let the lasagna rest for 10 minutes before slicing and serving.