You are right about LH etc. They used to serve BHX as part of the failed Euro-Hub at CGN in the early 1990s. Not sure about Birmingham European - did they ever serve CGN (they were DUS regulars, weren't they?).
The X3 loads to CGN are not exactly terrible. The average this year has been 77 pax - which is hardly 50% in a B737, but would make it a good route for a 100seater.