Stir together flour, salt, and baking powder in a medium bowl; set aside.
In an electric mixer with a paddle attachment, mix sugar, butter, shortening until light and fluffy on a medium speed, about 2 minutes.
Add eggs one at a time, beating well after each addition. Then, mix in the lemon zest. Add in the vanilla extract, corn syrup, and lemon extract. Mix until well combined.
On low speed, add half of the flour mixture and mix, scraping down the sides of the bowl as needed. Mix in the sour cream then stir in the remaining flour mixture until smooth.
Divide the dough into 2 portions and wrap around with plastic wrap. Refrigerate for at least 6 hours and up to 2 days.
Preheat oven to 350ºF. Grease a baking sheet with spray or line with parchment paper or baking mat.
Take a dough from the refrigerator out on to a lightly floured surface. Roll the dough into 1/4-inch thick. Using a cookie cutter, cut out the dough and transfer to the prepared baking sheet. Work fast while the dough is still cold. Repeat with the other piece of the dough.
Bake for 8-10 minutes or until the edges of the cookies turns slightly gold. Let the cookies stand in a baking sheet for 1 minute, then transfer to wired racks to cool completely.
When cookies are cool, drizzle the icing on the cookies. Let cookies stand until the icing set, at least 2 hours.