Preheat your oven to 350°F (175°C) and line two cookie sheets with parchment paper.
In a small bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Set this dry mixture aside.
In a larger bowl, beat the softened butter and 1 cup of granulated sugar until the mixture is light and fluffy. This should take about 3-4 minutes.
Add the lemon juice, vanilla extract, and egg to the butter mixture, and mix until well combined.
Stir in the lemon zest from 2 lemons, mixing until just incorporated.
Gradually add the flour mixture to the wet ingredients, mixing after each addition until the dough is fully combined.
In a small bowl, combine the remaining ½ cup of sugar with the zest from the third lemon.
Using a cookie scoop, form the dough into tablespoon-sized balls. Roll each ball in the lemon sugar mixture and place them on the prepared cookie sheets, spacing them about 2 inches apart.
Bake the cookies for 10-11 minutes, or until the tops no longer look wet and cracks begin to form. Avoid over-baking for a soft texture.
Allow the cookies to cool on the cookie sheets for 5 minutes before transferring them to a cooling rack.