This was a source of much criticism for a while and was explained to us during SMD1 in a Q&A session.
Essentially, none of the wireless internet in any of LH's German ports (and quite possibly in other ports) is free of charge, with the exception of the First Class lounges in FRA and MUC (AFAICT). All of it is chargeable; T-Mobile customers can streamline the process of gaining access.
The long and short is that LH entered into a long term contract with T-Mobile to provide wireless internet in its lounges, however there was a charge instituted for its use. The contract was created quite some time ago when having any wireless internet - free or not - was considered novel. The upside is that LH garnered a lot of good attention for early adoption of providing wifi in lounges, but as the adoption of wifi proliferated very quickly and later made for free, LH couldn't wiggle or renegotiate its T-Mobile contract.
I imagine that a new contract is looming soon and hence it will be provided for free.
Oddly enough, except for some hotels, it is quite common for wifi to not be free anywhere in Germany. I have no idea of the culture behind this.