Preheat your oven to 350°F and line a baking sheet with parchment paper. This gives your oven time to reach the proper temperature while you prepare the dough, ensuring even baking from the moment the cookies go in.
In a medium bowl, combine the lemon cake mix, vegetable oil, and room-temperature eggs. Zest the lemon directly into the bowl, then cut the lemon in half and squeeze the juice through a fine sieve to remove pulp—add about 2-3 tablespoons of fresh lemon juice to the mixture. Add the salt and stir everything together until just combined; the batter will be thick and slightly lumpy, which is perfect. I find that room-temperature eggs blend more smoothly into the dry cake mix, creating a better texture in the final cookie.
Transfer the cookie dough to the refrigerator and chill for 15-20 minutes. This resting period allows the flavors to meld and makes the dough much easier to scoop and shape without sticking to your hands.
Pour the powdered sugar into a shallow bowl. Working with the chilled dough from Step 3, scoop walnut-sized portions using a cookie scoop or small spoon and roll each piece between your palms into a smooth ball. Immediately roll each ball in the powdered sugar to coat all sides, then place on your prepared baking sheet about 1½ inches apart. I like to coat just a few cookies at a time so the powdered sugar stays dry and doesn't clump—if it gets damp, it won't adhere as nicely.
Bake in your preheated 350°F oven for 9-11 minutes, until the edges are lightly golden and the centers still look slightly underbaked. The cookies will continue to cook slightly on the hot pan after removal, so don't overbake them or they'll become dry.
Remove the baking sheet from the oven and let the cookies sit on the pan for 2 minutes to firm up slightly. This brief rest keeps them from falling apart when you move them. Transfer the cookies to a wire cooling rack and let them cool completely. They'll firm up as they cool and develop a tender, cake-like crumb with a slight crispy exterior.