I came across the city name of "Libege" when doing genealogy research.
Is Libege a historical spelling of the modern-day city of Liège?
Source (among others): Geneagraphie family tree
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No, I can find no evidence that Libege is a real place. I think it is simply a spelling error for Liège on that family tree that has been perpetuated on several other family tree websites.
However you can be fairly certain that the author meant Liège by taking a quick look at the Wikipedia page for the same person.
Well according to the sources to https://fr.wikipedia.org/wiki/Louis_De_Geer_(1587-1652) he was indeed born in Liège.