Working with 1 zucchini at a time, cut lengthwise into very thin (julienne) strips with slicer, turning zucchini and avoiding core. Discard core. Toss zucchini strips with 1 teaspoon salt and let drain in a colander set over a bowl, covered and chilled, 1 hour. Gently squeeze handfuls of zucchini to remove excess water and pat dry with paper towels. Cook corn in a small saucepan of boiling water until tender, about 3 minutes. Drain, then rinse under cold water and pat dry. Whisk together lemon juice, sugar, pepper, and remaining 1/4 teaspoon salt in a large bowl, then add oil in a slow stream, whisking. Add zucchini, corn, tomatoes, and basil and toss well.