Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the lemon cake mix and instant lemon pudding mix. Whisk until well combined.
Add the eggs, vegetable oil, lemon juice, lemon zest, and vanilla extract to the dry ingredients. Mix until just combined; the dough will be thick and sticky.
Cover the bowl with plastic wrap and chill the dough in the refrigerator for about 30 minutes.
Line your baking sheet with parchment paper.
Once chilled, use a spoon or cookie scoop to portion out the dough. Roll each portion into a ball and coat in confectioners sugar.
Place the sugar-coated dough balls on the prepared baking sheet, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are set and the tops are crinkled.
Remove the cookies from the oven and let them cool on the baking sheet for about 5 minutes before transferring to a cooling rack.
