Preheat the oven to 350 degrees. Line a baking sheet with a silpat mat.
In a large bowl, beat the butter and sugar together with a mixer until creamy. Add the vanilla, egg, lemon juice, and lemon zest and beat until smooth and well mixed. Combine the flour, salt, baking powder, and baking soda together until well combined. Slowly add the flour mixture to the lemon mixture until mixed. The dough will be very sticky. Place into the refrigerator for 10-15 minutes or until firm enough to roll into balls.
Roll the dough into small balls then toss in the bowl of powdered sugar until evenly coated. Place the balls on the baking sheet about 2 inches apart. Place into the oven and bake for 9-11 minutes.
Remove the cookies from the oven and let them cool on a wire rack for at least 7 minutes to set.
Serve the cookies immediately with a tall glass of ice cold milk. Enjoy!