Whisk the flour, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with a mixer on medium speed until light and fluffy, about 3 minutes. Add the eggs, one at a time, beating well after each addition. Beat in the lime zest and juice, then beat in the food coloring. Reduce the mixer speed to low; gradually add the flour mixture, beating until just combined. Cover and refrigerate until firm, about 45 minutes.
Position racks in the upper and lower thirds of the oven; preheat to 350 degrees F. Line 2 baking sheets with parchment paper. Combine the confectioners' sugar and sanding sugar in a small bowl. Roll tablespoonfuls of dough into balls and toss in the sugar mixture to coat completely. Arrange the cookies 2 inches apart on the prepared baking sheets.
Bake, switching the pans halfway through, until the cookies are puffed and cracked on top and golden around the edges, 18 to 20 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.