You will need to clear security and I *think* customs/immigration - as I am a German citizen I really don't pay attention as it takes me seconds to clear.

MUC is a wonderful airport, and a fitting tribute to a great Bavarian hero. I would definitely leave the gate/lounge area for that amount of time; either to sleep/shower at a hotel, or at least to walk in the sunshine and shop in the mall. The shower waits can be over an hour and up to two hours in the lounge, and there is much better to do with your time there.

That is actually enough time to even get to a local hotel in Freising if you like. My family uses the Kempinski when flying out of MUC, but I stay offsite and it doesn't take long. (I agree with going downtown, but having done the India flights I also agree with the need to rest/shower in between)

Also, note that LH lounge access is NOT available to non-members, even spouses, I believe (you may want to confirm on the LH Miles and More board of this website) I often seen angry UA members' companions being turned away in FRA and MUC