In a large bowl, whisk together the flour, lemon pudding mix, salt, baking powder, and baking soda. Set aside.
Place 1 ½ cups of the white sugar, the brown sugar, and the lemon zest in the bowl of a stand mixer. Mix on medium speed for 20 seconds to release the lemon oils into the sugar.
Add the melted butter and mix until smooth, about another 20 seconds.
Mix in the eggs, lemon juice, and vanilla extract until fully combined and smooth.
Gradually add the flour mixture to the wet ingredients. Mix on medium-low speed just until combined – avoid overmixing to keep the cookies tender.
Scrape down the bowl, give it a final mix for 2 seconds, then cover with plastic wrap. Refrigerate for 2 hours or up to overnight.
When ready to bake, preheat your oven to 375°F (190°C) and line two large baking sheets with parchment paper.
Place the remaining ½ cup of white sugar on a shallow plate for rolling the dough balls.
Scoop the dough into 2 1/2-ounce balls, roll them evenly in your hands, then roll in the sugar to coat.
Arrange the dough balls about 1 ½ inches apart on the prepared baking sheets.
Bake on the oven’s upper and lower racks for 15-18 minutes, rotating pans halfway through. Cookies should spread, crackle on top, and be golden around the edges.
Let cookies cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.