Your story reads very similar to mine. I have a great grandfather that we cannot get behind. His name was John and he suddenly appeared in the 1871 Canadian census.
He was Alsatian and he also gave no clue to his past, in oral tradition. He married a Barabara Moseburger in Waterloo County Ontario Canada. From here I have all the rest of the Family. In the Lorentz Family the name John is used so widely it is hard to locate the John your are looking for.
I would bet if there is a connection there must be some sort of correspondance from or to Waterloo County Ontario Canada.This might be the place to start.