Preheat oven to 350°F. Spray a 12-cup bundt pan with nonstick cooking spray (the kind with flour) or butter and flour it.
Use a hand or a stand mixer to beat the cake mix, butter, eggs, milk, extract, and pudding mix until a thick batter forms. Pour into prepared pan.
Bake for 35-45 minutes, or until a toothpick comes out with just a few crumbs. Remove the cake from the oven and cool for 10 minutes but keep it in the pan.
While the cake is baking, make the sauce. Melt butter in a small saucepan over medium low heat. Stir in the sugar, lemon juice, zest and salt and cook until it just simmers (bubbles around the edges). Remove from heat and stir in the vanilla.
Poke several holes in the cake using a long skewer and pour the butter sauce over the cake. Cool in pan completely, then remove to serving plate. Dust with powdered sugar before serving.