Using a sharp-shaped vegetable peeler, peel zucchini lengthwise. To cut ribbons, hold the zucchini in one hand and peeler in the other, peel long, wide strips lengthwise. Once it becomes hard to handle, place zucchini, cut side down, on board; continue peeling. Transfer to a large bowl; toss with coarse salt. Let sit until zucchini releases some of its liquid, about 10 minutes. Pour off accumulated liquid; blot zucchini dry with paper towels.
Meanwhile, in a small bowl, whisk together fresh lemon juice and olive oil; season with salt and ground pepper. Pour mixture over zucchini. Add mint leaves and red onion; toss gently, and serve immediately.