Hello Gothik and welcome to the forum.
That drive you have is an OEM LG model. These models are typically tailor made (the features are typically different from retail LG models) for companies who ship them with computers they sell. The way it works is that these companies who sell the drives in computers have to support them with firmware updates as well. LG itself does not provide firmware updates or support for these OEM models as it only supports retail models.
I do not know why an OEM model was available in a local shop for sale as a bare unit. It should not have been available for purchase without a system, because you effectively, have no firmware updates or support for it.
As for why that firmware update refused to work, I’m not sure. What is known is that OEM models made for one computer manufacturer may not be the same as for another. If your GWA-4161B was actually made for say Fujitsu, it may not be the same as the GWA-4161B made for HP/Compaq. Because of that, the firmware for the same model from one computer manufacturer may not work with the same model of drive from another computer manufacturer. That is about the only thing I can think of.
Unfortunately, that HP/Compaq firmware is about the only firmware I have ever come across for the GWA-4161B. Sad to say, but I don’t think there is any solution here.