Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add zucchini, cover, and steam until tender, 7 to 8 minutes. Drain.
Place basil leaves, pine nuts, and garlic in a food processor; pulse briefly until ground together. Add zucchini, 2 1/2 tablespoons olive oil, 2 tablespoons Parmesan cheese, lemon juice, salt, and pepper; pulse until combined. Pour in remaining 2 1/2 tablespoons olive oil through the feed tube and pulse until pesto is smooth.
Bring a large pot of lightly salted water to a boil. Cook gnocchetti in the boiling water, stirring occasionally, until tender yet firm to the bite, about 9 minutes. Drain, reserving a few tablespoons of cooking water.
Toss gnocchetti with zucchini pesto in a bowl. Thin with reserved cooking water. Garnish each serving with 1 teaspoon Parmesan cheese.