Using large mixing bowl, combine powdered sugar and butter. Use electric mixer to cream together.
Add lemon juice, lemon zest, and vanilla and mix until well blended.
Add eggs one at a time and beat on low speed until thoroughly mixed.
In separate smaller bowl, combine flour, baking powder and baking soda and stir with fork.
Gradually add dry ingredients to egg mixture and beat with mixer until just blended, use a soft spatula to scrape sides and bottom of bowl to ensure thorough mixing.
Drop by tablespoon onto parchment paper line baking sheet.
Bake for 18-20 minutes, or until cookies are light golden in color and set.
Use hard spatula to remove from baking sheet and place on cooling rack.
for the icing
Using small sautée pan, heat butter, lemon juice, and vanilla over low heat.
Gradually stir in powdered sugar to desired consistency.
Use pastry brush to apply icing to tops of cookies.