Preheat the oven to 325 degrees. Line baking sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter until creamy. Gradually add 1/2 cup of confectioners' sugar and 1/4 teaspoon lemonade Kool-aid powder. Beat on medium-high speed until light and fluffy. Mix in the lemon juice, zest, and salt. With the mixer speed on low, add the flour in three additions, mixing until incorporated and scraping down the bowl after each addition.
Scoop the dough by the tablespoon and roll each dough portion into a ball. Place each cookie on the prepared baking sheets, at least one inch apart, and gently flatten the dough balls with the palm of your hand.
Bake for 15 to 20 minutes, until cookies are lightly browned at the edges. Cool on the baking sheet for 10 minutes, then transfer cookies to a wire rack to cool completely.
In a small bowl, combine the remaining 1/2 cup of confectioners' sugar and 1/4 teaspoon lemonade Kool-aid powder. Dip the cooled cookies into the lemonade sugar. Store cookies in an airtight container in the refrigerator.