Yes, the purpose of this trip if for job interviews with LH. This is why it is priority "b" (which, as I have now been informed, does not stand for "business" :-)). The interviews are all fixed in terms of time so it is not like I can take a flight a week later. I HAVE to fly on that day. I will make sure to point that out to the gate agent.
I have LH M&M FTL status which should help, according to the reservations agent. The last time I flew internationally in Economy is many years ago, and since I will have job interviews right after it would be really nice to fly in C or F. I suppose you get used to the comforts of C/F :-). Will the FTL status help then? Maybe?