Stir together the flour, sugar and salt in a large mixing bowl. On a board, roll the butter and cheese together until it is small, crumbly pieces. Blend in with the flour, cayenne and salt, adding the egg, and blending in water as needed, until mixture forms a dough ball. Wrap tightly in plastic wrap and chill for ½ hour.
When chilled, set the dough on a lightly floured board and roll out to a size to fit the bottom and size of a 9-inch tart pan. Place the pastry shell in the pan, press in gently and prick the bottom and sides in a few places.
Bake for 10 minutes, remove and let cool. Once cool, remove shell prom pan. Set aside.
Lower the oven temperature to 350 degrees.
For the filling:
Raise the oven temperature to 400 degrees.
While pastries are cooking, prepare the filling. Separate the egg whites from yolks. In a medium bowl, beat the egg yolks until thick. In a separate bowl, beat the egg whites and lemon juice until slightly firm. Return to the bowl with the yolks, and stir in the mayonnaise, mustard, dill, salt, pepper and crab. Gently stir the crab mixture in with the egg whites mixture. Spoon into the pastry shells. Bake for 8 to 10 minutes or until browned.