Line a baking sheet with parchment paper and set aside.
Make lemon sugar. Add the lemon zest to the sugar in a small bowl, and use your fingers to rub them together. Do this until the sugar seems almost wet. (The oils from the zest will release into the sugar, which adds more of the lemon flavor to the cookies.
1 cup granulated sugar, ¼ cup Meyer lemon zest
Mix dry ingredients. Combine the flour, baking soda and baking powder in a large bowl. Whisk to blend and set aside.
2 cups all-purpose flour, ½ teaspoon baking soda, ½ teaspoon baking powder, ½ teaspoon kosher salt
Mix wet ingredients. In another bowl, combine the melted butter, olive oil, vanilla, lemon-sugar and salt. Mix just until until it’s smooth. Add the eggs and whisk again just until smooth. Then whisk in the lemon juice.
½ cup unsalted butter, melted, 2½ tablespoons olive oil, 1 tablespoon pure vanilla extract, 2 large eggs, ¼ cup Meyer lemon juice
Mix wet with dry. Use a large spoon or spatula to fold the wet ingredients into the bowl with the dry ingredients. Only mix until you no longer see dry spots.
Shape and refrigerate. Use a 1¼ inch cookie scoop to shape the batter into small mounds, onto the parchment-lined baking sheet as you so. They can be close together at this point. Cover the baking sheet with plastic wrap and refrigerate for at least 6 hours (and up to 2 days).
Prep powdered sugar and set oven. After the refrigeration time, or when you’re ready to bake, preheat the oven to 350°F, add the sifted powdered sugar to a shallow bowl, and line another baking sheet with parchment paper.
⅔ cup powdered sugar, sifted
Roll the dough into balls. One by one, roll the shaped dough between your palms to form smooth balls. If they are sticking to the parchment, use a small flat-bottomed spatula to help release them.
Coat with powdered sugar. After each one is shaped, drop it into the powdered sugar and roll it until it’s completely and generously coated with it. Place them about 3 inches apart on the newly lined baking sheet as you go. (You will likely only fit about 12 per sheet — between batches, return the shaped dough to the refrigerator.)
Bake and cool. Bake in the preheated 350°F oven use until the edges look the slightest bit golden, about 13 minutes. Let them sit for at least five minutes on the baking sheet, and then transfer them to a baking rack to cool to room temperature.