Jpatokal - You should have lounge access, even intra-EU as a *Gold. Check with the LH lounge. If they won't allow you to store your baggage, see if you can go ahead and check your bags with your next leg, just leaving you with your carry-on.
Six hours is just enough time to get into the city, have a good meal and a liter (or two), and take a look around. Just as a previous poster mentioned, I'd stick to the Marienplatz area.