Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large bowl, cream together the softened butter and granulated sugar until light and fluffy, about 3-4 minutes.
Beat in the egg, vanilla extract, lemon zest, and lemon juice until well combined.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Using a tablespoon, drop rounded balls of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.
While the cookies cool, prepare the filling by mixing together the powdered sugar, softened butter, and lemon juice until smooth and creamy.
Once the cookies are completely cool, spread a generous amount of the lemon filling on the flat side of one cookie and top it with another cookie to create a sandwich.
Repeat with the remaining cookies and filling.