Preheat the oven to 350 degrees F and line a cookie sheet with parchment paper.
In a large bowl, combine the white cake mix, cake flour, butter, egg, lime juice, and lime zest. Mix until well combined.
Scoop the dough with a small cookie scoop and place on the prepared cookie sheet. Bake for 15 minutes, or until the edges are lightly browned.
Let the cookies sit on the cookie sheet for 5 minutes, then transfer to a cooling rack and cool completely before glazing.
Glaze
In a medium bowl, combine the powdered sugar, lime zest, lime juice, and milk. Mix well. If the glaze is too thick, add more milk 1 teaspoon at a time until it reaches a drizzling consistency.
Drizzle over the cooled cookies.
Notes
Best served cold. Store airtight at room temperature up to 1 week; the refrigerator keeps them firmer.
Freeze the dough in balls, or freeze baked cookies unglazed and glaze after thawing.
Swap the lime for lemon or orange to change the flavor. [Lucy: confirm butter state, softened vs melted.]