Whisk the vinegar, lemon juice, garlic, and thyme in a large bowl to blend. Season with salt and pepper. Gradually whisk in the oil. Spoon 3 tablespoons of the marinade into a small bowl. Cover and set aside. Add the zucchini and yellow squash to the remaining marinade in the large bowl and toss to coat. Transfer the mixture to a 13 by 9 by 2-inch glass baking dish. Cover and marinate at room temperature at least 3 hours or cover and refrigerate up to 1 day.
Prepare the barbecue for medium-high heat. Grill the vegetables until they are crisp-tender and brown, turning occasionally, about 8 minutes. Transfer the vegetables to a platter. Drizzle with the reserved marinade and serve hot or at room temperature.