Preheat the oven to 350ºF or 175ºC. Grease an 8-inch square pan and line it with wax paper.
In a large bowl, sift together the flour, baking soda, salt, cloves, and cinnamon. Set aside. In a second large bowl, stir together the applesauce, brown sugar, oil, and stout. Mix thoroughly. Add the flour mixture, a little at a time, beating well after each addition.
Stir in the raisins, dates, and walnuts.
Spoon the batter into the prepared pan and bake for 40 to 45 minutes, or until a skewer inserted in the center comes out clean. Remove from the oven and cool on a wire rack for 10 minutes. Invert the pan onto a plate, remove the wax paper, and set the cake upright to cool completely.
To make the icing:
In a large bowl, combine the butter and lemon zest. Sift the sugar into the butter and beat with an electric mixer until smooth and creamy. Stir in enough lemon juice to make the icing soft enough to spread easily.
Spread the icing on top of the cake and smooth the surface with an offset spatula or knife dipped in warm water. Decorate the top with lemon slices, if desired.