Preheat your oven to 350°F. In a bowl, whisk together the all-purpose flour, baking powder, and salt. Set this mixture aside.
In another mixing bowl, combine the butter and sugar. Beat them together until the mixture is smooth and creamy.
Add in the egg, vanilla, lemon juice, and lemon zest into the butter and sugar. Stir until everything is well combined.
Gradually mix in the dry ingredients from your first bowl. This dough will be somewhat dry and crumbly but should press together easily.
Now, roll the dough into small 1″ balls and smooth them gently between your hands. Place the balls on a parchment paper-lined baking sheet.
Bake the cookies for about 10 minutes, or until they are set but not browned. Once they are done, let them cool on a wire rack.
For the glaze, take a bowl and slowly add the lemon juice to the powdered sugar. Stir until the mixture reaches a nice pourable consistency.
Drizzle the lovely glaze over each cooled cookie and allow the glaze to set completely. Once set, transfer your cookies to an airtight container for storage.