In the bowl of a heavy duty electric mixer, stir together flour, sugar, lemon peel and salt. Make a well in the center of the flour mixture and pour the beaten eggs into it. Using the paddle attachment of the mixer, beat the flour mixture on low speed just until combined.
Distribute the butter pieces, sour cream and 2 tablespoons of vegetable oil evenly over the top of the flour mixture. On low speed, beat until blended. Scrape the bottom of the bowl. Pour the water over the dough. On medium low speed, beat the dough for 10 to 15 minutes until dough is smooth and elastic. If necessary, scrape the dough off the paddle occasionally.
Gather dough into a ball, lightly dust with flour and wrap tightly in plastic wrap. Refrigerate for 8 hours or overnight.
Pour enough oil into a large skillet so that it is 1 inch deep. Heat the oil to 350. While oil is heating, roll out the cookies.
Cut the dough into quarters and keep the pieces refrigerated until ready to roll out. Pat a piece of dough into a square that is 1/16 inch thick. Cut the square into diamonds by cutting into 1 1/2 inch wide diagonal strips, first in one direction and then in the opposite direction.
Using a metal spatula, carefully lift the diamonds up and transfer them to a baking sheet lined with waxed paper. Refrigerate the diamonds until you're ready to fry them. The dough is soft, and once it's chilled you can reshape the diamonds if they get distorted while being lifted.
Fry the cookies about 12 at a time until they puff up and turn golden brown, about 2 to 3 minutes on each side. Transfer cookies to paper towels to blot up excess oil. Cool slightly. Generously dust with confectioners' sugar. Repeat with remaining pieces of dough, adding more oil if necessary.