Preheat oven to 350°F. Line two baking sheets with parchment.
Cream butter, granulated sugar, and brown sugar until fluffy, about 2 minutes.
Beat in lemon zest, lemon juice, and vanilla until smooth.
Mix in applesauce until fully combined.
Whisk flour, oats, baking soda, baking powder, salt, and cornstarch in a bowl.
Add dry ingredients to the wet mixture. Stir just until no dry streaks remain.
Fold in white chocolate chips if using. Let dough rest 5–10 minutes.
Scoop tablespoonfuls onto sheets, spacing 2 inches apart.
Bake 10–12 minutes, until edges set and tops look dry.
Cool 5 minutes on sheets, then move to a rack to finish cooling.