Preheat the oven to 325 degrees F (165 degrees C). Grease and flour a fluted tube pan (such as Bundt®).

Sift together flour, baking powder, and salt into a bowl.

Combine sugar and butter in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs, 1 at a time, beating well after each addition. Add flour mixture in 3 batches, alternating with sour cream, beating batter briefly after each addition. Stir in lemon zest and pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 55 to 60 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Invert carefully onto a serving plate or cooling rack. Let cool completely, about 1 hour.

Stir 3 teaspoons lemon juice, powdered sugar, and butter in a small bowl until a thick glaze forms. Drizzle glaze over the cooled cake.