Sorry to revive an old post, but OP did you manage to get the MUC-LIS segment added to your existing ticket?

I'm trying to do something similar right now. I have a confirmed booking SIN-FRA SQ saver award (booking class I) and want to add an FRA-MUC connection on LH. An hour on the call center resulted in variations of "it's not allowed", "I can't see the availability" (you can find it online on the SQ or any *A website), and "I can see it but it's only in economy so I can't ticket it." They also refused to escalate me to someone who could help out.

I could go to ION but I won't be back in Singapore for another 10 days so there's the risk that the FRA-MUC availability disappears. Of course it's ridiculous that in 2023 you have to go to a physical ticket office to get decent customer service.