Spread half the chopped onion over the bottom of a large bowl. Cover with separated crab lumps and then the remaining onion. Season with salt and pepper. Add the oil and vinegar. Strain the ice through a sieve to remove the ice cubes, then add the well-chilled water to the salad. Cover and refrigerate for at least 2 hours and up to 12 hours. Toss lightly, then taste and adjust for seasoning with salt and pepper before serving.