Make the marinade: Heat oil, lemon zest, and garlic in a small saucepan until bubbling around the edges. Remove from heat, and let cool completely. Stir in lemon juice. Season with 1/2 teaspoon salt and 1/4 teaspoon pepper.
Make the pesto: Puree pine nuts and garlic in a food processor until a paste forms. Add basil, and pulse to combine. With machine running, pour in oil through feed tube until pureed. Season with salt and pepper.
Heat grill to medium. Assemble the "lasagna": Arrange tofu on a double layer of paper towels. Cover with another double layer of paper towels, then cover with a baking sheet. (Weigh it down with 2 cans or something else equally heavy.) Let stand for 20 minutes.
Meanwhile, brush zucchini and squash slices with oil, and season with 2 teaspoons salt and 1/4 teaspoon pepper. Grill, flipping occasionally, until softened and slightly charred, about 8 minutes. Remove from grill. Whisk marinade, and drizzle half of it generously over zucchini and squash slices.
Repeat with tofu and remaining marinade, flipping occasionally, until nicely charred, about 3 minutes. Let cool slightly. Slice tofu horizontally into 1/8-inch-thick sheets (they will be layered, so don't worry if they fall apart).
Lay 3 slices each of zucchini and squash on a platter to form a 6 1/2-by-8-inch rectangle. Spread 3 tablespoons pesto over tops. Cover with a layer of tofu, and season with salt and pepper. Top with a layer of tomatoes, and season with salt and pepper. Top with 6 large basil leaves. Repeat layering twice (zucchini and squash, pesto, tofu, tomatoes, basil). Serve cold or at room temperature.
Pesto can be refrigerated for up to 3 days. Bring to room temperature before using. Assembled "lasagna" can be refrigerated overnight.