| Prepare grill for indirect-heat cooking over medium-hot charcoal (high heat for gas).
Trim squash and halve lengthwise, toss with salt, pepper, and 2 tablespoons oil in a bowl. Oil grill rack, then grill vegetables directly over hottest part of coals, covered only if using a gas grill, turning over once, until grill marks appear, about 6 minutes. Move vegetables to area of grill with no coals underneath and grill, covered, until tender, about 4 minutes more. Transfer to a platter. While vegetables are grilling, whisk together lemon juice, mustard, sugar, and remaining 2 tablespoons oil in a small bowl. Pour dressing evenly over vegetables before serving.
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