In the bowl of a stand mixer fitted with the paddle attachment, cream the 1 cup unsalted butter, 1 ½ cups granulated white sugar, and zest of 4 lemons together on high speed until light and fluffy. This should take about 2 minutes.
Add the 2 large eggs, 2 tablespoons lemon juice, and 1 teaspoon vanilla extract. Mix on medium speed until combined. Scrape down the sides of the bowl.
Add the 3 cups all-purpose flour, 1 teaspoon baking soda, and ½ teaspoon kosher salt. Mix just combined being careful to not overmix.
Fold in the 1 ½ cups white chocolate chips with a rubber spatula.
Wrap the cookie dough in wax paper and refrigerate for at least 3 hours. The chill time allows the dough to firm up and allows the flour to fully hydrate.
Preheat the oven to 350°F (180°C). Remove the dough from the refrigerator and roll it into balls, about 2 tablespoons of dough each. The dough may be a bit crumbly but will become smoother as you roll it.
Place the balls on an ungreased cookie sheet leaving at least 2 inches in between each cookie. Flatten the balls slightly with your hand to help them spread.
Bake for 10-12 minutes or until the edges are lightly golden brown. Allow the cookies to cool for at least 5 minutes before transferring them to a wire rack cooling to cool completely.
Once they have cooled, use a flour sifter or fine mesh strainer to dust the cookies with the ¼ cup powdered sugar.