Preheat oven to 350°F (175°C) and line baking sheets with parchment paper.

In a large bowl, cream together softened butter and powdered sugar until light and fluffy.

In a separate medium bowl, whisk together all-purpose flour and salt.

Gradually add the dry ingredients to the butter and sugar mixture. Mix until just combined and a dough forms.

Turn dough out onto a lightly floured surface and knead a few times to bring it together into a ball.

Roll out dough to about 1/4-inch thickness.

Cut out shapes using cookie cutters.

Place cookies on prepared baking sheets, leaving about an inch between them.

Bake for 12-15 minutes, or until edges are lightly golden.

Let cookies cool on baking sheets for a few minutes, then transfer to a wire rack to cool completely.

While cookies cool, whisk together powdered sugar, fresh lemon juice, and lemon zest in a small bowl to make the glaze. Adjust consistency with more lemon juice or powdered sugar as needed.

Once cookies are completely cool, dip the tops in the glaze or drizzle it over them.

Let the glazed cookies sit undisturbed until the glaze has set completely, about 30 minutes to an hour.