Preheat the oven to 350 degrees F (175 degrees C). Generously grease a large fluted tube pan (such as Bundt®).
Blend cream cheese and shortening in a large mixing bowl with an electric mixer until creamy. Beat in sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Add flour, milk, lemon zest, baking powder, and salt. Mix on low speed just until thoroughly blended, scraping down the sides of the bowl occasionally. Pour into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 45 to 50 minutes.
While the cake is baking, mix sugar and lemon juice until sugar is dissolved.
Remove the cake from the oven. Pour the lemon glaze over the hot cake, allowing it to run down the edges between the cake and the pan. Cool in the pan for 30 minutes. Remove from the pan and cool completely.