For the cookies, preheat the oven to 350 degrees Fahrenheit and lightly grease cookie sheets or line them with nonstick baking mats.
In the bowl of an electric mixer, combine cake mix, vegetable oil, egg, lime and lemon juice, and lime and lemon zest until incorporated.
Form or scoop dough into 1 1/2" balls and place at least 2" apart on prepared cookie sheets. Press the dough balls down with the palms of your hands to flatten. Bake for approximately 8 to 9 minutes. Mine were done at 8. Don't overbake or they won't be soft! Allow them to cool for a few minutes on the pan and then carefully remove them to a cooling rack to cool completely.
To make the glaze, whisk together powdered sugar, lime and lemon zest, and lime and lemon juice. Add milk very carefully and slowly (I only needed about 1/2 tsp.), as necessary for thinning. Drizzle over cooled cookies. Serve.