A customer told me they wanted marble icing. Does anyone have a clue to what it is?

is she perhaps speaking of marbled fondant or buttercream???

Well, back in my country there is a MARBLE ICING that is made by mixing 8 egg whites, 8 kilos of confectioners sugar, 1 tablespoon of lemon and 1 tablespoon of flavoring
Mix all together and keep ading more conf. sugar (you will need more than 3 kilos) until you have a fondant consistency
Then you add this icing peace by peace, smoothing over with your hands (I also use the wilton fondant smoother).
I have a link to a youtube video that teaches this technique..
if that's what you're looking for, let me know and I will post the link to you
that's sounds weird but it sure is tasty.