Preheat oven to 350°F. Line two baking sheets with parchment.
Beat butter, sugar, and lemon zest until pale and fluffy.
Whisk the beaten egg with vanilla and lemon juice. Beat into the creamed mixture.
Stir flour, baking powder, baking soda, and salt together. Add to the bowl and mix just combined.
Chill dough 10 minutes if sticky for easier scooping.
Scoop tablespoon portions onto sheets, spacing about 2 inches apart.
Bake 10–12 minutes, until edges set and centers look soft.
Cool 5 minutes on the sheet, then move to a rack.
Whisk powdered sugar with lemon juice to form a drizzleable glaze.
Glaze cooled cookies. Let set before serving.