Preheat the oven to 350 degrees. Line a sheet pan with parchment paper.
In a mixing bowl, combine the cake mix, eggs, and oil. Stir until well combined.
Using a 1-tablespoon cookie scoop, portion the dough onto the sheet pan. Bake for 8 minutes until just set. The cookies should NOT turn brown on top. Let the cookies cool on the pan for 5 minutes before transferring to a cooling rack.
For the frosting, add the powdered sugar, butter, and lemon juice to a small bowl. Start with the juice from ½ of the lemon, depending on how lemony you want the frosting. If necessary, you can add a squirt of milk (or more sugar) to get the spreading consistency you desire.
Using an offset spatula, spread the frosting on the cookies. Let the frosting set up before storing in an airtight container. Separate the layers with parchment paper. The cookies will keep for up to 4 days.
Notes
For an 18.25-ounce box cake mix, increase oil to ½ cup.