Position an oven rack in the center of the oven and preheat to 475 degrees F. Lightly coat a pizza pan or stone with nonstick cooking spray and put on the rack. (If you don't have a pizza peel or a way to transfer the pizza, skip placing the pan in the oven to preheat and prepare the pizza right on the pan.)
Toss the zucchini ribbons with 1/8 teaspoon salt and place in a colander over the sink. Let drain for 15 minutes to remove excess water. Pat the zucchini dry with a paper towel or kitchen towel. Toss with 1 tablespoon lemon juice, half of the zest and 1 teaspoon olive oil and set aside.
Wrap the tomato slices in a paper towel and gently press down, removing excess water. Set aside.
Stretch the pizza dough into a round large enough to fit on the pizza pan (or directly on the pan, if not using a pizza peel). Whisk together the ricotta, chives, remaining tablespoon lemon juice, remaining zest and 1/8 teaspoon each salt and pepper.
Spread the ricotta over the prepared dough, leaving a small border for the crust. Evenly scatter the tomato slices and zucchini ribbons over the ricotta. Lightly drizzle with the remaining 2 teaspoons olive oil and sprinkle with Parmesan and additional chives.
Bake until the crust is golden brown and the cheese is bubbly, 12 to 15 minutes. Serve.