Preheat the oven to 350 degrees F. Prepare the baking by lightly greasing with vegetable shortening or line the pan with parchment paper.
Combine the sugar, butter, and sour cream with an electric mixer beat on medium speed until the mixture is creamy and well blended.
Add the eggs, lemon zest, and lemon juice and continue to beat until the mixture is well mixed.
Mix together the flour, baking powder, and salt and add it to the wet ingredients. Using the electric mix on low-speed mix the batter until the dry ingredients are mixed in.
Drop by rounded teaspoons onto the prepared baking pan about two inches apart.
Place the cookies into the preheated oven and bake for 10 to 12 minutes or until the edges of the cookies are lightly browned.
Remove from the oven place the baking pan on a cooling rack and let the cookies sit for 1 to 2 minutes. Remove from the baking pan and set the cookies on the cooling rack and cool completely.
Once the cookies are cooled prepare the icing.
Beat the powdered sugar and enough of the lemon juice until the icing is the right consistency for spreading. Gradually add the lemon juice do not add all at once.
Store in an airtight container.