Marinating lump crab overnight gives it terrific flavor; combining it with a scallion-and-paprika-spiked mayonnaise makes it even more delicious.
Spread half of the chopped onion in a large bowl. Top with the crab, season with salt and pepper and cover with the remaining chopped onion. In a small bowl, whisk the oil with the ice water and 1/3 cup of the vinegar. Pour over the crab, cover and refrigerate overnight.
In a medium bowl, combine the mayonnaise with the lemon juice, paprika and the remaining 1 tablespoon of vinegar. Drain the crab and fold it into the mayonnaise, along with the scallions and parsley. Garnish with the red onion and serve with toast points.