Preheat oven to 350 degrees F. In metal bowl, combine sugar and flour. In another bowl, lightly beat the eggs and add them to the sugar mixture, combining well. Blend the butter into the mixture using the back of a spoon. Add the buttermilk and blend with a whisk. If the butter has not incorporated by this step set the bowl over a pan of simmering water to help soften the butter. Add the lime juice, vanilla and nutmeg. Blend well. Slowly pour the custard filling into the pie crust. Set the pie on a baking sheet and place it in the oven for 1 hour. Remove pie and let it cool before cutting.
Combine the butter, shortening, 2 cups of the cake flour, and 1 cup of the all-purpose flour. Blend together. Stop mixer, scrape the sides and add remaining 2 cups of cake flour and remaining 1 cup of all-purpose flour. Blend to combine completely. Mix sugar and salt into 1/4 cup of the water and add it to the flour mixture. Blend briefly and add the remaining water if needed. The dough should not be overworked and should make a solid piece when held in your hand. Turn the dough out onto a lightly floured smooth surface and knead it several times. Divide the dough into portions and flatten it. Wrap unused dough in plastic. Roll out the dough to fit a 9-inch pie pan. Reserve any unused dough in the freezer for another use.
Preheat oven to 475 degrees F. Prick bottom and sides of pastry with fork. Bake 12 minutes or until light brown. Cool on wire rack.