Preheat oven to 350 degrees
In a stand mixer, with a paddle attachment, cream together butter, confectioner's sugar, and granulated sugar
Add in confectioners sugar and cream together again
Add in water, vanilla, lemon juice, eggs, and mix on low speed for 30 seconds
In a separate bowl, combine baking soda, cream of tartar, salt, and flour, and whisk together.
Slowly combine wet and dry ingredients in stand mixer bowl.
Mix until combined, and dough comes away from the bowl edges. The dough should not be very sticky.
Roll into balls approximately 2 Tbs of dough
Using a glass, smash down the balls so the cookies are flat and edges crinkle. Try to keep cookies consistent so they cook evenly. The place where the glass was will make a shallow well, which is great for frosting the cookies later.
Bake 6 to a tray, for 8 minutes, the cookies should be slightly browned on bottom.
Remove from tray immediately, and let cool completely,
Mix together frosting ingredients in a mixer. Sift powdered sugar so you don't get lumps (I was in a hurry and didn't, and you can see a few lumps in mine.
Once cookies are cooled, frost, and enjoy!