Preheat oven to 350°F (175°C). Spray a bundt pan with baking spray (such as Baker’s Joy), or grease and flour the pan.
In the bowl of a stand mixer fitted with the paddle attachment (or in a large mixing bowl if using an electric hand mixer), combine sugar and lemon zest. Use your fingers to rub the zest into the sugar for about 30 seconds, or until the sugar is fragrant.
Add the dry pudding mix and mayonnaise to the sugar, then use the mixer to beat them together.
Add the eggs to the mixture, then mix until incorporated, scraping down the sides of the bowl as needed.
Add the flour, baking powder, and salt to the bowl, mixing on low speed just until combined.
Add the milk, then mix on low speed until incorporated well.
Spread the batter evenly in the prepared bundt pan. Bake in preheated oven for 42-45 minutes, or until a toothpick inserted in the center of the cake comes out clean.
Remove from oven and let the cake cool in the pan for about 10 minutes, then run a knife along the sides of the pan to loosen the cake from the pan. Invert the cake onto a serving plate.
Prepare the glaze by combining powdered sugar and lemon juice in a small mixing bowl. Whisk together until smooth. Brush or drizzle the glaze over the top of the cake, then let sit for at least 15 minutes to allow the glaze to set to a satiny finish.
Allow cake to cool, then slice and serve.