Preheat oven to 350 degrees. Line 2 cookie sheets with parchment paper.
In a small bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
In a larger bowl, beat the butter and 1 cup sugar until the mixture is combined and light in texture. Pour in the lemon juice, vanilla and add in the egg. Add in the lemon zest from 2 lemons and mix until just combined.
Slowly add in the flour mixture, mixing between each addition, until both mixtures are well combined.
In a small bowl, mix together the 1/2 cup sugar and the zest from the 3rd lemon.
Using a cookie scoop, form the dough into tablespoon sized balls and roll in the sugar/lemon mixture. Place on the cookie sheet 2 inches apart.
Bake for 10-11 minutes, until the tops are no longer wet looking and cracks start to form. Allow the cookies to cool for an additional 5 minutes on the cookie sheet and then transfer to a cooling rack or wax paper.
Store in an airtight container.