Preheat an outdoor grill for high heat. When hot, lightly oil grate.
Combine the squash, zucchini, onion, and bell pepper in a bowl; drizzle with olive oil; sprinkle with lemon-pepper seasoning; stir to coat. Place the vegetable mixture in the center of a large sheet of aluminum foil. Top with another large sheet of aluminum foil. Roll the edges of the foil sheets together to seal into a packet.
Place the packet on the preheated grill. Cook until the vegetables are tender, about 30 minutes, turning the packet every 5 to 10 minutes.