As suspected, the latest order of Sankt Martini Church records did show that the two ARNECKE women that married Karl LANKAU had the same father, so they are at least half-sisters. The name of their mother(s) is a little up in the air at the moment, but because the same surname (OEHME) was listed, it may be an issue with how she was referred to from record to record. The Sankt Martini records are extremely consistent, though, so it may be that David ARNECKE married two OEHME sisters.
The Church records also show that widower David ARNECKE married widow Maria Anna van BORNBERGER (née FRANKE) in 1842. The marriage record states that his parents were Johann Heinrich Wilhelm ARNECKE and Justine RASEHORN of Cattenstedt (southwest of Halberstadt). There is no FHL film for Cattenstedt.
I found the baptism record of who I believe to be the elusive Karl/Carl/Charles LANKAU that immigrated with Emil in 1881; the Karl LANKAU that apparently immigrated at New York, settled in St. Louis, then moved back east to New Jersey. Emil and Karl were in fact half-brothers. The surprise was that Karl's mother was not one of the ARNECKE sisters, but rather a Maria Dorothea BIELERT. So, Emil's father Karl had at least three wives and nine children.
I doubt any additional Halberstadt church records are going to help with the LANKAU family. I'm not sure how to efficiently proceed with finding the family in Magdeburg, even though I am quite curious about that migration. Identifying the correct church in Halberstadt so quickly was a bit of luck.
Johann Christoph OEHME, resident of Kühlinger Straße no. 682, Halberstadt, died in 1850 at the age of 82. I have not translated the notations yet, but I believe this man will end up being the father of Johanna Sophie Justine (OEHME) ARNECKE, Emil LANKAU's maternal grandmother. The key detail is the address (Kühlinger Straße no. 682), which was referenced in several ARNECKE and LANKAU records.
[genealogy, Arnecke, Lankau, Oehme, Cattenstedt, Halberstadt, Magdeburg]