In a large mixing bowl, cream together shortening and sugar until a thick paste forms.
Add eggs, one at a time, with the mixer running. After last egg is added, turn mixer to high speed and beat for 30 seconds. Scrape down the sides of the bowl and mix to combine.
Add add lemon extract and dry ingredients. Mix until a dough forms. The dough will be thick and sticky. Drop dough, a generous 1 1/2 Tablespoons on prepared cookie sheet.
Bake for 18-20 minutes or until the cookies are light colored and "puffy." (When you pick up a finished cookie, it should be light and have a brown bottom.) Transfer cookies to a wire rack to cool.
Make the Icing: When cookies are cool, make the icing. In a small mixing bowl, combine ingredients. Stir until icing is smooth. If the icing is too thick, add a teaspoon or two more water.