Preheat the oven to 325°F (165°C). Generously coat a 12-cup bundt pan with nonstick baking spray and set aside.
In the bowl of a mixer, beat the butter, shortening (or oil), and cream cheese on high for about 2 minutes until combined and smooth. Gradually add the granulated sugar while continuing to beat on high for about 7 minutes, until the mixture lightens in color and becomes fluffy.
Add the eggs one at a time, beating briefly after each addition and scraping down the bowl as needed so everything is evenly incorporated.
Reduce the mixer to its lowest speed and add the sifted cake flour in two portions. Once the flour is mostly incorporated, add the salt, key lime zest, and key lime juice, mixing just until blended—avoid overmixing to keep the cake tender.
Stir in the vanilla extract, scrape the sides and bottom of the bowl, and mix briefly to ensure a uniform batter.
Pour the batter into the prepared bundt pan, smoothing the top. Bake for 1 hour and 15–25 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to rest in the pan on a wire rack for 10 minutes. Invert the pan onto a serving plate or rack and let the cake cool for at least one hour, or until it is cool to the touch.