You need to buy a ZED with LH and if the flight is full you list for jumpseat at the gate. You will most likely be put in a FA jumpseat or directly behind the cockpit in the crew rest jumpseat.
I work in the Union as a Jumpseat rep and I have talked to LH directly about this. If you are a pilot and in uniform they will give you a cabin Jumpseat or the cockpit at the discretion of the Capt but I they will not do this for every US based airline make sure your JS reps talk to LH. This is the same with Singapore Airlines.
Singapore Airlines are great they have sent reps to the ALPA meeting in DC to talk about how they can set up JS in the Asia region. While its a long way off its good to see a company like SQ showing support.