Line a baking sheet with parchment paper.
1) Mix together the butter, sugar, grated lime rind, lime oil, and salt; there's no need to beat at high speed, just mix together.
2) Mix in the flour. Cover the dough, and refrigerate for about 1 hour, or as long as overnight. Just before baking, preheat the oven to 325°F.
3) Remove the dough from the fridge, and scoop teaspoonfuls onto the baking sheet, 1 1/2" apart.
4) Bake the cookies for 12 to 14 minutes, until set and lightly brown around the edges.
5) Remove from the oven, and let cool for 10 minutes.
6) Put the sugar in a 1-gallon zip-top bag.
7) Add 5 or 6 warm cookies at a time, and shake gently till they're coated. The sugar may get a bit sticky; that's OK.
8) Transfer the cookies to a rack to cool, then coat the completely cooled cookies in the sugar again.