since there seems to be some mystery about where the family came from originally, it is all the more important to try to find them in the church records.
For examply, at a birth there is typically a Godparent whose name, relationship and town would have likely been recorded. So, if either Lambert or Wilhelmine's family members (or both) would have served, you now have an additional location to look perhaps.
Additionally, if they were protestant, and the older kids would have been confirmed during the time when they lived in Duisburg, then often the confirmand's birth and birth located may have been recorded in the confirmation records.
Thus, providing you perhaps another avenue to identify their earlier place of birth or residence.