Apparently it's most likely tied to the German municipality of Waake or the Swedish tribe of Vagoths. However most Lithuanians would likely explain it in the form of a joke - either about Germans being thieves ('vogti' = to steal) in reference to Teutonic/Livonic ordins, or about them being 'tough' or well armored ('vo kiets' ~= 'wow, tough/hard').
Another fun fact: at least in Croatia, we colloquially call them "schwabs" which originates from another group of germanic people https://en.wikipedia.org/wiki/Suebi
It comes from the fact that Germany didn't unify until very late, so the people were called by the small city-states that they came from. In American revolutionary war, some British mercenaries were called Hessians....
According to Wikipedia [1], it’s a matter of some debate, with the theories being the (standard) corruption of a name for the first Western Baltic people encountered, or a take on the “unintelligible war cry” people from the Latvian root for speaking.