Thanks, all. Any way you cut it, it's clear I'm not sleeping in that morning. ;-)

Isn't flying fun nowadays!

If it's very early there may be no agents at the ticket counter as others have found. Maybe Lufthansa is different and they'll be open earlier than other airlines.

But if it's like Air France in Basel we passengers were very early (by 5 a.m.), but no agents were there until 6 a.m. The Swiss-based airline next to Air France had their ticket counters operating already.