Dressing fish for dressing: Combine vinegar and sugar in heavy small saucepan. Stir over low heat until sugar dissolves. Remove from heat. Add ice cubes and stir until melted. Puree cilantro, lemongrass, fresh ginger and sesame oil in processor until smooth. Gradually mix in vinegar mixture. Season dressing with salt and pepper. (Can be made 4 hours ahead. Cover tightly and refrigerate.)
For Fish: Place fish in small baking pan. Pour 1 ½ C dressing over. Cover and refrigerate 45 minutes. Prepare barbecue (medium-high heat) or preheat broiler. Bring 3 C water to boil in medium saucepan. Stir in rice and salt. Reduce heat to low, cover and cook until water is absorbed and rice is tender, about 20 minutes. Remove from heat and keep covered. Meanwhile, cook sliced carrots in large pot of boiling salted water 3 minutes. Add broccoli florets and cook 2 minutes. Add trimmed snow peas and cook until vegetables are just crisp tender, about 1 minute. Drain well. Transfer to large bowl. Toss vegetables with foil to keep warm. Grill fish until just cooked through, about 4 minutes per side. Divide rice among 4 plates. Top with fish. Arrange vegetables alongside and serve.