Add the dough ingredients to a stand mixer bowl, using the dough hook attachment. Mix until it's a smooth, elastic mass.
Prepare the filling by combining lemon zest and sugar, then mixing in softened butter.
After your dough has proofed, roll it into a large rectangle on a floured surface, and spread the lemon filling evenly. Roll up the dough, making a tight, even spiral.
Slice the roll into pieces and arrange in a baking dish. Bake until golden brown.
While baking the rolls, mix all your icing ingredients in a large mixer bowl. Run on low speed until you get a creamy consistency.
Spread the icing on top of baked lemon buns. Serve warm.