Preheat your oven to 350°F (175°C). This ensures that your cookies bake evenly.
In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.
In a large mixing bowl, beat the room temperature butter with the brown sugar and granulated sugar until the mixture is light and fluffy.
Mix in the instant lemon pudding mix, followed by the eggs one at a time. Add the vanilla extract and lemon zest, mixing until fully combined.
Gradually add the dry ingredients to the butter mixture, mixing until just combined.
Gently fold in the quick cooking oatmeal and white chocolate chips. Make sure they are evenly distributed throughout the dough.
Using a cookie scoop or tablespoon, drop rounded balls of dough onto a baking sheet lined with parchment paper, spacing them about 2 inches apart.
Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden. The centers may look a bit soft, but they will firm up as they cool.
Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely.