Preheat oven to 325°. Beat butter and shortening at medium speed with a heavy-duty electric stand mixer until creamy. Gradually add sugar, beating at medium speed until light and fluffy. Add eggs, 1 at a time, beating just until blended after each addition.
Stir together flour, baking powder, and salt. Add to butter mixture alternately with milk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Stir in vanilla, lime zest, and lime juice. Pour batter into a greased and floured 10-inch (12-cup) tube pan.
Bake at 325° for 1 hour and 15 minutes to 1 hour and 20 minutes or until a long wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 to 15 minutes; remove from pan to wire rack.
Prepare Key Lime Glaze, and immediately brush over top and sides of cake. Cool completely (about 1 hour).