Pre-heat oven to 350 degrees.
In a medium bowl, whisk together the flour, baking soda, salt, and lemon zest.
In the bowl of an electric mixer or other large bowl with a hand mixer or whisk, beat the butter and sugar together, until light and fluffy, about 3 minutes.
Add in the egg, vanilla, and lemon juice and mix until combined.
Slowly mix in the flour mixture until just combined, taking care not to over-mix.
On an un-greased cookie sheet, drop dough by the tablespoon about 1 inch apart.
Bake the cookies for about 15-20 minutes, until edges are golden. Let cool for a couple minutes on the cookie sheets before transferring to wire racks to cool completely.
When cookies are completely cooled, spread with lemon glaze.