Beat together the cream cheese and milk in a large bowl with an electric mixer until smooth, about 2 minutes.
Combine the crabmeat, water chestnuts, mustard, onion, Worcestershire, soy sauce, lemon juice, 1/2 teaspoon salt and a few grinds of pepper in a medium bowl and toss gently to combine.
Spread out the cream cheese mixture in an even layer in a 9- by 13-inch baking dish. Spread the sweet-and-sour sauce on top, leaving about a 1-inch border of cream cheese all around. Spoon the crab mixture on top of the sweet-and-sour sauce. The dip can be prepared up to this point and refrigerated, covered, overnight.
Just before serving, scatter the lettuce, scallions and cilantro over the crab, leaving a 1-inch border all around. Serve with wonton skins, shrimp chips or rice crackers.