I can't give the exact loads at the moment (maybe its already a bit late as you've already departed) but of the cuff, I can say June 4th being a Sunday and the middle of a long weekedend at that, shouldn't be a problem. Friday June 9th is a different matter. Early morning domestic flts are nomally full(like anywhere else in the world) Also don't forget thats when the Word Cup starts! I would seriously contemplate taking the train. The following is a toll number in Germany for info on LH loads, its euro 1.25 per minute: 0190 770199. In Germany don't even bother calling ticketing or reservations office. And as an aside, you don't need to be listed for LH inner-german flights