In a large bowl, toss zucchini and carrots with lemon juice, 1 tablespoon oil, 3/4 teaspoon salt, and 1/4 teaspoon pepper. Cover and chill. Marinate, gently tossing 2 or 3 times, 8 hours or overnight; drain well, reserving marinade. Meanwhile, put almonds in a large bowl, cover with 2 inches water, and set aside to soak 8 hours or overnight; drain well.
In a food processor, puree almonds, garlic, and 2 tablespoons oil until smooth; transfer to a large bowl and set aside. In the same processor (no need to clean it), working in batches as needed, pulse kale and basil, scraping down the sides often, until very finely chopped; transfer to bowl with almond mixture. Add yeast, if using, 1/2 teaspoon salt, and 1/4 teaspoon pepper, stirring to combine; set aside.
Toss spinach with reserved zucchini marinade, squeezing with your hands to wilt it; wring dry, and discard marinade. Puree tomatoes in a blender until smooth; season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
To assemble lasagna, alternate layers of zucchini and carrots with kale-almond mixture and spinach, making 4 layers of each, in a 9" x 13" dish. Arrange beets on top, then scatter fennel over beets.
Serve immediately, or chill for a few hours first. It can be consumed cold or at room temperature. To serve, pour some of the tomato puree onto each plate, then top with a piece of lasagna. Garnish with chervil and pepper to taste, and drizzle with remaining 2 tablespoons oil.