To make the icing, whisk together the confectioners’ sugar and lemon juice. Add 1 tablespoon of milk or cream and whisk until smooth, then add by the teaspoon until you reach the desired consistency. Add salt to taste.
Spoon the icing over the completely cooled cake, using the back of the spoon to gently smooth it over the top of the cake and letting it drizzle a bit down the sides. Sprinkle with lemon zest. Allow the icing to set before serving. Cover and store any leftover cake for up to 4 days in the refrigerator.