In the bowl of a stand mixer, beat the butter, 1 cup of the sugar and salt until smooth. Add all of the lemon juice and half of the zest. On a low speed, add the flour, 1/2 cup at a time, until just incorporated. Turn the cookie dough out onto a board and roll it into a log. Cover with plastic wrap and refrigerate for at least 1 hour and up to 24 hours.
Preheat the oven to 350 degrees F.
Remove log from the refrigerator and cut it into thin 1/4-inch thick discs. If using 1 baking sheet, bake the cookies in batches. Arrange the discs on 2 silicone or parchment lined baking sheets, 1-inch apart, and bake until the edges are just golden, about 20 minutes. Remove the cookies from the oven and transfer them to a wire rack to cool completely.
Meanwhile, using stand mixer or hand mixer, mix cream cheese with the remaining 1 cup confectioners' sugar and remaining half of the lemon zest.
Top half of the cookies with the cream cheese mixture and cover with another cookie to make a sandwich. Dust the top of the cookie sandwiches with confectioners' sugar and serve.