My great grandfather Lorenz(Larenz) Zaucha
There are number of Slavic and Slovenian names that had been incorporated into German. In the article in German, entitled "Slavic and Slovenian (Alpine Slavic) names of places in Austria, wwwg.uni-klu.ac.at/spw/oenf/name1.htm, the author provides a short dictionary of "some Slovene (Slavic) words that form Austrian village, mountain and river names" (the names are either in Slovenian orthography or listed in their common Slavic form).
Here I just list them, without explanation: bel, bister, blato, bor, brdo, breg, breza, dol, gor, gora, grad, holm, javor, ledina, les, lipa, loka, pleš, pleša, polje, raven, ravna, reka, riba, selo, sedlo, suh, suha.
As you see, one of them is "suh" (dry, withered) and "suha" (stream bed without water). It appears as dialectal Zauchen in Austrian place names, such as Zauchen, Zauchensee, etc.
So the Zaucha surname could have been derived from "suh" or "suha" - corresponding to "suchy", "sucha" in Polish, meaning dry.
Oh, I missed these two:
I have found the marriage records in Canada for my grandfather Lorenz Zaucha. The records show his name as Wawrzenie Zawicha
Should be Wawrzyniec, not Wawrzenie. Wawrzyniec is indeed the Polish version of Vavřinec (Czech), Vavrinec (Slovak), Laurentius (Latin), Lawrence (English), Lorenz (German)
L orenz Zaucha parents were Wogociech and Maryna Zawicha from Austria Poland
Should be Wojciech, not Wogociech. Wojciech is a Polish version of Slavic "the joy of war", Vojtěch (Czech), Vojtech (Slovak). The name has been rendered into German in several different variations including: Woitke, Witke, Voitke, Voytke, Woytke, Vogtke, Wogtke, Woetke, and Wötke.
It is commonly accepted that the Latin (or rather German) equivalent name is Adalbert, but their components and meanings are in fact completely different. The two names may have become associated as a result of St Adalbert of Prague (born Vojtěch Slavník) taking the name of Adalbert at confirmation.
en.wikipedia.org/wiki/Wojciech
L orenz Zaucha parents were Wogociech and Maryna Zawicha from Austria Poland
I checked the Zawicha name in "Moi Krewni" database. Not such name appears there. There are however 930 surnames Zaucha in Poland, most of them in city of Tarnów and Tarnów region - 359, moikrewni.pl/mapa/kompletny/zaucha.html.