Preheat oven to 375°F (190°C).
Arrange zucchini planks on paper towels and sprinkle lightly with salt; let sit for 10 minutes to draw out moisture, then pat dry.
In a medium bowl, crumble the pressed tofu by hand until it reaches a curd-like consistency.
Mix the crumbled tofu with nutritional yeast, lemon juice, oregano, minced garlic, salt, and pepper until thoroughly combined.
Spread 1/2 cup of marinara sauce across the bottom of a 9x13 inch baking dish.
Place a single layer of zucchini planks over the sauce, overlapping slightly.
Spread half of the tofu mixture over the zucchini, followed by a layer of spinach and 1/2 cup of marinara sauce.
Repeat the layers: zucchini, remaining tofu mixture, spinach, and marinara sauce.
Top with a final layer of zucchini, the remaining marinara sauce, and the vegan mozzarella shreds.
Cover the dish with foil and bake for 30 minutes.
Remove the foil and bake for an additional 15 minutes until the zucchini is tender and the cheese is melted.
Let the lasagna rest for 10 minutes before slicing to allow the structure to set.