The final dough will be slightly softer than most cookie dough. For the best results, handle the dough as briefly and gently as possible when shaping the cookies. Overworking the dough will result in flatter cookies.
Preheat oven to 350°F Line 2 baking sheets with parchment paper.
In a medium bowl, whisk together the flour, coconut, baking soda, baking powder, and salt. Set aside.
Combine 1 1/2 cups of sugar, the lime zest, and cream cheese in a large bowl. Put the remaining 1/3 cup sugar in a pie plate and set aside. Pour the warm butter over the cream cheese mixture and whisk to combine - the mixture won't be completely smooth yet. Whisk in the oil then the egg, milk and lime juice. Mix until smooth. Use a rubber spatula to fold the dry ingredients into the wet, until a soft dough comes together.
Portion the dough onto the prepared baking sheets with a cookie scoop, using about 2 tablespoons for each cookie. Working quickly (if you handle the dough too much you're more likely to wind up with flat cookies), roll the dough into a ball with your hands then roll in the sugar set aside in the pie plate previously. Repeat until you've used all of the dough, placing 12 cookies on each baking sheet. Use the bottom of a glass to flatten the dough balls into discs that are about 2 inches in diameter. Sprinkle the tops of the cookies with the remaining sugar in the pie plate, using about 2 teaspoons per sheet of cookies.
Bake the cookies, 1 tray at a time, for about 11-13 minutes, or until the edges are set and beginning to brown. The tops will be puffy and slightly cracked. Transfer the baking sheet to a wire rack and let the cookies cool on the sheet for 5 minutes then transfer them to the rack to cool completely.