Preheat the oven to 400°F. Line baking sheets with parchment paper or silpat mats and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with an electric mixer, cream together the shortening and sugar until light and fluffy, about 3 full minutes.
Add in the egg, vanilla, buttermilk, water, lemon juice and lemon zest and mix until the ingredients are fully incorporated.
In a medium bowl, whisk together the flour, baking soda and salt. Slowly add the dry ingredients to the wet mixture and mix on medium-low speed until just combined, being careful not to overmix.
Use a small cookie scoop (about 1 tablespoon) to drop batter onto prepared cookie sheets about 2 inches apart. Bake for 6-7 minutes in the preheated oven.
Allow cakes to cool on baking sheets for 5 minutes then transfer to wire racks to cool completely.
While cooling, make the cream cheese frosting. In a large bowl using a handheld or stand mixer fitted with a paddle attachment, beat the cream cheese and butter together on high speed until smooth and creamy, about 2 minutes. Add 3 powdered sugar, vanilla, and salt. Beat on low speed for 30 seconds, then switch to high speed and beat for 2-3 minutes until thick and smoth.