I consider Lufthansa a pretty good airline. Only once did I have a somewhat rough confrontation with a very rude flight attendant. But this is an anecdote, not a statistic....
Regarding German airports, on the other hand, I have just recently had very AWFUL experiences. Both in Berlin and Munich.
In Munich there was a line something like 500 m long (I swear!) inside the airport, because all entrances gates were not working except one. I didn't miss my plane only because by chance, I had arrived there several hours early...
In Berlin something very similar. I risked missing the plane there as well. I asked the attendants on the ground if they could let me through, and they completely ignored me, even though I showed them my ticket. They told me "ask the other passengers, we can't do anything about that". Note that there too I had arrived HOURS early - as suggested by friends - and also the train from Berlin had arrived as usual late.
Maybe I was just unlucky but German infrastructure is notoriously in sharp decline. I work for a German company, and this is the opinion of my many German friends and colleagues, not mine.
Bottom line: no problem with Lufthansa IMHO, but be careful to arrive VERY early at the airport!