To me it seems to be clear that the original name was "Ciocco", with a pronouciation very similar to Ziock. This means: Ciocco was renamed to a name fitting better to the German language. When this has happenend exactly and where must be found out.
Most of "Cioccos" today live and in the past lived in Switzerland: Graubünden, Grisons, situated at the italian border! These emigrants were called "the Welsch" from Bünden; they were thousands. Most of them were artisans, e.g. masons, lithotomes, painters and - why not - glasers.
This is just one trace into your personal past and without a promise of success. If you kwow more: Please let kwow about it. You find the Cioccos in the Phone-list of Switzerland and in the Mormon' s records.
By the way, the old Lerners lived in Switzerland, too. But more about that maybe later.
Your' sincerely Horst