Kind of looked over some of your other posts. In response to your other post, I don't recall the present day pastor Schliemann's first name.
Have you figured out which of your Schliemanns were born in Germany (your immigrant ancestor)? What was his/their name(s) if you know the middle names even better as many were given several names and did not always go by the first one they were given, birthdate (as much as you know), birth place (at least the answer on the census like Mecklenburg or Pommern, or Prussia etc), was he married here or there, approximate immigration year? These are the things needed to do a comparison to see if there is a match your person(s).
I know of two major Schliemann groups -- the one related to the archealogist (forgive my spelling here, I'm being lazy in not checking it) and another from Mecklenburg-Schwerin. I think mine likely connect to this later group as they are in the same area but alas I have not found the connection yet.