Heat oven to 350 degrees F. Line 2 large baking sheets with parchment paper.
In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
In the bowl of a stand mixer fitted with a paddle attachment, cream the butter and sugar at medium speed until light and fluffy, about 3 minutes. Scrape down the sides of the bowl with a rubber spatula as needed. Add the egg, vanilla extract, lemon juice, and lemon zest and beat at medium speed until combined, about 30 seconds. Add the dry ingredients and beat at low speed until just combined, about 30 seconds, scraping down the bowl as needed.
Place the powdered sugar in a shallow bowl. Roll a heaping tablespoon of dough into a 1½-inch ball, roll the ball in the powdered sugar mixture, and place it on the prepared baking sheet. Repeat with the remaining dough, spacing the balls about 2 inches apart.
Bake, rotating sheets halfway through, until cookies are set in center and begin to crack, 10 to 12 minutes. Let cookies cool on sheets for 3 minutes before transferring cookies to wire racks to cool completely.