Adjust the rack to the center position of the oven and preheat the oven to 375°F. Grease a rimmed 18x13x1-inch half sheet pan with softened butter.
In a large pot set set over medium heat, melt the butter. Add the water and the lemon juice, increase the heat, and bring to a boil. Remove pot from the heat and allow to cool for at least 5 minutes. Then briskly stir in the flour until smooth, followed by the sugar, sour cream, and lemon zest. Stir in the eggs until fully incorporated (temper them first if the batter is still hot). Mix in the vanilla and lemon extract. Then sprinkle the baking soda and salt over the top of the batter (make sure there are no lumps!) and stir them in until all ingredients are well blended.
Pour the batter into the prepared sheet pan and smooth the top. Bake for 15 to 18 minutes or until a toothpick inserted into the center of the cake comes out clean. Cool the cake completely before glazing.
For the glaze, measure the powdered sugar into a bowl and stir in the lemon juice until completely smooth. Add a bit more lemon juice if the glaze is too thick or a little more powdered sugar if it's too thin. Pour the glaze over the cooled cake and immediately spread into a thin, even layer. If desired, garnish the cake with small lemon pieces of lemon. Chill (uncovered) for at least 30 minutes to allow the glaze to set before slicing. Cover tightly and refrigerate any leftovers.