Surely BA didn't let you book a through ticket over LCY!
They certainly would sell me this (I wouldn't have come up with it on my own!) - ba.com lists it as the final connection of the day from ARN to FRA - BA8492 leaves ARN at 16.55, in to LCY at 18.25, out again at 19.20 on the BA8736, arriving FRA at 21.50.
The previous connection leaves ARN at 15.40 (over an hour earlier), via LHR (in 17.15, out 19.10) and arrives FRA at ... wait for it, 21.55 (five minutes
after the LCY flight).
5711N0205W, I take your point about flying direct with Lufthansa but (a) it suits me to collect the BA miles at the moment, (b) the one-way fares from ARN to FRA with LH are a bit breath-taking .. just over 8000 SEK one-way "Economy Flex". For that price I can fly Club Europe with BA ... return ... twice! (almost)