Thanks for your reply.

Since it took a while before anybody came up with an answer and I had some time to spare at the office, I went up to the staff travel office at my airline myself and asked them how it worked.

Seems they just issue a regular ZED ticket (so for travel in Y clas) and LX just 'knows' that it should upgrade SN staff to C class whenever possible, just as it does with its own staff (and in return SN does the same to LX staff then).
As such, whenever switching to another airline, we should just expect a seat in Y class there indeed, but then we've only paid for Y class as well.

Now, the agreement between SN/LX dates back to the Sabena/Swissair days, but with SN (now Brussels Airlines) and LX under the same roof again (that of LH: Lufthansa), there's a change it might also come to include LH in the future indeed.
As far as I know LH staff can travel in C class on standby basis at their own airline: anybody around here knows whether that's also valid for LX staff when flying LH (and vice versa)? If it is, then that's good news for me... :-)