Preheat the oven to 425 degrees F. Put a rack on a baking sheet.
Use a mandoline or vegetable peeler to make ribbons from the entire length of each zucchini, as wide as possible (the first few may be too skinny). Make 48 ribbons total (you should get 12 from each zucchini). Lie the ribbons flat on the rack on the baking sheet (it's ok if they overlap slightly) and sprinkle with 1 teaspoon salt. Let sit for 10 minutes, then pat completely dry with paper towels.
Put the tomatoes in a large bowl and toss with the Italian seasoning, 1 tablespoon of the olive oil, 1 teaspoon salt and a few grinds black pepper. Arrange the tomatoes cut-side down in a 9-by-13-inch baking dish. Bake until soft to the touch and some of the juices have been released, about 25 minutes.
Meanwhile, mix the ricotta, mozzarella, goat cheese, lemon zest, 1 teaspoon salt and a few grinds black pepper in a medium bowl. Lay out 2 zucchini ribbons lengthwise and slightly overlapping, then top with 2 more ribbons crosswise and slightly overlapping, to make a cross. Spoon a heaping tablespoon of the cheese mixture in the middle of the zucchini cross. Tightly fold the zucchini over the cheese mixture one ribbon at a time, alternating between the crosswise strips and the lengthwise strips, so you end up with 1 zucchini square. Repeat with the remaining ribbons and filling. Drizzle with the remaining tablespoon olive oil and season with salt and pepper.
Put the zucchini packs on top of the roasted tomatoes and bake until the zucchini is softened and the cheese is melted, 10 to 12 minutes.
Meanwhile, toss the arugula with the lemon juice and divide among 4 plates. Spoon the tomatoes and zucchini onto the plates and drizzle with olive oil.
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