*G members can access the LH lounges at Munich. Some have showers its just a matter of finding the right ones. Might want to ask on the LH forum.

From the LH website:

Even after you leave the aircraft, our message is: a warm welcome! We invite you to freshen up in one of our lounges after a long-haul night flight or prepare for the day's business. We offer lounges with showers at Frankfurt, Düsseldorf, Munich and New York (JFK) airports, as well as refreshing drinks, newspapers and magazines, a business center, and TV and restrooms.