Preheat oven to 350℉. Prepare a large baking sheet with a non-stick spray, or parchment paper, set aside.
In a medium bowl whisk the flour, baking soda, salt, and lemon zest.
In large mixing bowl beat the butter for a few seconds, add the sugar and mix until light and fluffy. Add in the egg, vanilla, and lemon juice. Mix until fully combined.
Continue mixing while you add in the dry ingredients. Mix until fully combined.
Drop cookie dough by the spoonful onto the prepared cookie sheet. Bake until light golden on edges, approximately 12- 14 minutes. Remove from oven, let cool on the cookie sheet about 5 minutes and then remove to continue cooling on a wire rack.
Once cooled prepare the glaze by whisking the powdered sugar, lemon juice, and lemon zest together until well combined. Spoon onto the top of the cookies. Allow to sit and dry, glaze will harden.
Store cookies in airtight container at room temperature.