Preheat the oven to 325°F (163°C). Grease and flour a 12-cup Bundt pan and set aside.
In a medium bowl, whisk together the all-purpose flour and salt until evenly combined.
In another bowl, whisk together the 7-Up (or Sprite), eggs, grated lemon zest, and vanilla extract until blended.
Using an electric mixer, beat the softened butter, vegetable shortening, and granulated sugar on medium-high speed until light and fluffy, about 2 minutes.
Reduce mixer speed to low. Add the flour mixture to the butter mixture in two additions, alternating with the egg–7-Up mixture, beginning and ending with the flour mixture. Mix just until incorporated after each addition.
Pour the batter into the prepared Bundt pan, smoothing the top, and bake for 60 minutes or until a toothpick inserted into the center comes out clean.
Let the cake cool in the pan on a rack for 10 minutes, then invert onto the rack and cool completely.
For the glaze, whisk the powdered sugar, lemon juice, and milk together in a small bowl until smooth. Drizzle the glaze over the cooled cake.