Preheat the oven to 350 degrees Fahrenheit.
In the bowl of a stand mixer with the paddle attachment, cream the butter, shortening, sugar and lemon zest. Mix in the egg and lemon juice.
In a separate bowl combine the flour, baking powder, and salt. Slowly mix into the wet ingredients until just blended, scraping the bowl if needed. Dough will be soft and slightly sticky.
Scoop rounded Tablespoons of cookie dough a few inches apart onto a baking sheet covered with parchment paper or a silicone baking mat. Press cookie dough balls halfway down with a cup dipped in sugar.
Bake at 350 degrees Fahrenheit for 8-9 minutes. The edges should barely be browning and the top of the cookies should look matte, not shiny/wet. Allow to rest for a couple minutes before transferring to a wire rack to cool. Let cookies cool completely.
Meanwhile make frosting. Place the cream cheese and lemon zest in a mixing bowl. Using a hand mixer, beat until smooth. Gradually add the butter 2 Tablespoons at a time, and continue beating until smooth and well blended. Add powdered sugar and lemon juice (+ 1 drop yellow food coloring, if desired) all at once. Blend until just combined.
Place a coupler and round piping tip onto a pastry bag. Fill with frosting. Pipe frosting in a swirl pattern on top of the cooled cookies starting from the outside and finishing in the center. Cookies may be placed in an airtight container and refrigerated, or stored at room temperature depending on personal preference.