Preheat the grill to medium-high heat. In a large bowl, combine the zucchini, yellow squash, red bell pepper, yellow bell pepper, red onion, and cherry tomatoes.
Drizzle the vegetables with olive oil, and sprinkle with garlic powder, salt, and black pepper. Toss until the vegetables are evenly coated.
Place the vegetables on the grill and cook for about 5-7 minutes, turning occasionally, until they are tender and have grill marks. Remove from the grill and let cool slightly.
In a small bowl, whisk together the balsamic vinegar, Dijon mustard, lemon juice, and a pinch of salt and pepper to taste.
Once the grilled vegetables have cooled, combine them in a large serving bowl. Drizzle the lemon vinaigrette over the top and toss gently to combine. Garnish with fresh basil before serving.