In a large bowl, beat the sugar, 2/3 cup sour cream, shortening, egg, lemon zest and vanilla on medium speed until blended.
Beat in the flour, baking soda and salt on low speed. Divide the dough in half. Shape each half into a disk and wrap in plastic wrap. Refrigerate for 1 hour or until firm enough to roll.
Heat the oven to 375 degrees.
On a floured surface, roll each disk to 1/4-inch thickness. Cut into shapes with cookie cutters. Place 2-inches apart on an ungreased baking sheet. Bake for 8 to 10 minutes or just until set. Remove from the baking sheet to a cooling rack. Cool for 30 minutes.
In a small bowl, stir together the remaining 2 tablespoons sour cream, powdered sugar and lemon juice until thin enough to drizzle. Drizzle over the cookies.