My question is particularly about "Part 2: company specific examination". Are those tests and interviews all held in German or English?
diverine
I think it's most likely that the dyadic co-operation test will be conducted in German. In this test both team partners sit, side by side, in front of computer monitors, both have headsets and keyboards. Communicating over a push and talk connection they have to manage a task which can be described as distributing virtual items to bridges or lorries that have different capacities. Through the different runs both team members act both as PF and PNF (to put it in aviation vocabulary).
The VERDI tests are most likely to be done in German, too. I took part in the test but I must not disclose any details. However, I can give examples of typical test situations. As for the first test, think of a stewardess who, after a flight through most severe turbulence, is completely reluctant to fly again. Of course you need her as a crew member, otherwise you cannot fly the next leg. Your task is then to convince her to do her job again. The second and third test are rather standard airline tests.
Do I need to be almost as good as a native German speaker?
I must frankly say, I don't know Lufthansa's policy concerning that question.
What I can say is that I once met a Lufthansa pilot who was from the Netherlands and who had a remarkable accent. So, I would assume that an accent alone will not spoil your chances.
Furthermore an English accent is nothing unpleasant to German ears. I hope this will encourage you a bit.