Preheat the oven to 375°F (190°C) and line baking sheets with parchment paper.
In a medium bowl whisk together the all-purpose flour, baking soda, and salt; set aside.
In a large bowl, cream the room-temperature unsalted butter with the brown and granulated sugars using a stand or hand mixer, scraping the bowl sides occasionally, until light and fluffy.
Add the eggs and vanilla extract to the creamed butter and beat until fully incorporated.
Stir in the dry instant lemon pudding mix, then add the flour mixture and mix until nearly combined.
Add the quick-cooking oats and continue stirring until no streaks of flour remain.
Fold in the lemon zest and white chocolate chips until evenly distributed.
Use a medium cookie scoop to portion dough onto the prepared baking sheets, spacing cookies about 2 inches apart.
Bake for 9–11 minutes, or until the edges are lightly golden but centers remain soft.
Transfer cookies to a cooling rack and cool completely before serving.