Preheat your grill to medium-high heat, ideally around 400°F (200°C).

Using a mandoline or a sharp knife, slice the zucchini and summer squash into thin ribbons, about 1/8 inch thick.

In a large mixing bowl, combine the zucchini and summer squash ribbons with olive oil, lemon juice, salt, and pepper. Toss gently to coat.

Carefully thread the marinated zucchini and summer squash ribbons onto skewers.

Place the assembled skewers on the preheated grill and cook for about 12 minutes, turning halfway through.

Remove skewers from the grill and sprinkle with freshly grated Parmesan cheese while still hot.