Preheat the oven to 400 degrees F (200 degrees C). Line two rimmed baking sheets with parchment paper.
Cream sugar, shortening, and butter together in the bowl of a stand mixer on medium-high speed until light and fluffy, about 1 minute.
Mix in sour cream and lemon zest on low speed until no streaks of sour cream remain. Add eggs, one at a time, mixing on medium-low just until there are no streaks of yolk, and scraping down the sides of the bowl between additions. Add flour, salt, baking soda, and baking powder all at once and mix just to combine.
Drop by heaping tablespoons on the prepared baking sheets, about 2 inches apart.
Bake in the preheated oven until the tops are puffy and spring back when lightly touched with a finger, about 10 minutes. They should be light golden, with occasional spots of pale golden brown.