In a mixing bowl, cream the softened butter, powdered sugar, and lime zest until light and fluffy.
In a separate bowl, whisk together the flour and salt.
Gradually add the dry ingredients to the butter mixture, mixing until just combined. Be careful not to overmix.
Divide the dough in half and shape each half into a log about 2 inches in diameter. Wrap the logs in plastic wrap and refrigerate for at least 1 hour, or until firm.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Remove the dough logs from the refrigerator and slice into 1/4-inch thick rounds. Place the rounds on the prepared baking sheet, spacing them about 1 inch apart.
Bake for 12-15 minutes, or until the edges of the cookies are lightly golden. Remove from the oven and let cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.