In Austria there was a province called the Kingdom of Lodomeria and Galicia. I've found lots of references to Galicia but I can't find an actual map of Lodomeria. What is that place and where was it? Why did the Austrians choose that name instead of using the much more famous Galicia?
Habsburgs justified their appropriation of the PLC land during the partitions of Poland by claiming to be rightful heirs to an ephemeral Late medieval kingdom of Galich and Vladimir (latinized as Galicia and Lodomeria).
It's important to remember that at the time it was a completely artificial, made up term. The kingdom that the Austrian province was ostensibly a continuation of ceased to exist in the 13th century, and in any case it was only in the approximately same area. Actual Lodomeria (that is the city of Vladimir Volynsky) was never part of the province - initially it stayed Polish, later on it was annexed by Russia). So, the answer to your question is that Lodomeria was never an actual place. It was like initially Galicia a term made up to legitimize Austrian occupation. Unlike Galicia, it never actually caught on as the name of the area.