The LX team knew that a connection was tight due late incoming aircraft. Bag likely was in first container (LX last-in, first-off containers are usually 'priority'). Ground staff notified and altered to 'make connection'.
Bag was located ASAP and 'hand-carried' to the departing aircraft (possibly in boot of pax-transfer BMW) Schengen check was only 'departure' - id Passport and if Schengen, simply check picture. If not Schengen, stamp departure.
Rudolf is your uncle ...
This might happen to a VVVIP at other European airports, LX takes pride in making it work for all their customers.