Bumping -

So I'm arriving MUC in LH F from the US; MUC is my destination.
It sounds like I can access the Senator Lounge (or also the FCL?) in the non-Schengen departures area after clearing security, even without an onward boarding pass.

Then is there a way to get from non-Schengen departures to customs/immigration? Many airports segregate international arrivals (particularly in the US), but I'm guessing the whole Schengen side is sterile, both departures and arrivals and the pax can mix and then exit through immigration when they're ready?

TIA