This question is only about copies of the spear that's kept in Vienna, not the Roman one or any other that are connected with "original" Holy Lance. I'm making this research for the story I'm in the middle of writing
I'll answer this question with what I've found out during my research up to this time, but first I'll wait for other responses (according to what I've understood from different meta topics, that's the way I should do, but maybe I'm wrong, I've got no experience with this site).
In 1000, Holy Roman Emperor Otto III and duke of Poland, Boleslaw I Chrobry, met at the Congress of Gniezno, which was the first capitol of Poland. During the meeting, Otto III gave Polish prince the copy of Holy Lance, which (so called "original one", even if it's from 8th century) is recently kept in Vienna, as a part of Imperial Regalia. It was one of symbols of his acceptance for creation of Kingdom of Poland, which was part of Otto's idea for expanding Empire's influence in Eastern Europe, through allies with Poland and Hungary. While the wooden staff didn't survive the millenium, it's spearhead is still kept at Krakow's Wawel Castle.
Unfortunately the reliquary with a fragment of nail (from Jesus' cross, according to legends) was stolen (with much more of Polish crown treasure) by king John Casimir II from Swedish dynasty of Vasa, when he decided to leave Polish throne. He took it to Paris, where he became an abbot of Abbey of Saint-Germain-des-Prés. The relic finally vanished when the chapel was robbed during French Revolution, in 1793.
I know the story of Polish one well, the same with the one in Vienna and found some good Hungarian language sources on the St. Stephen's spear, at least until the 17th century. But there were few other copies and I would be very happy to receive any additional informations about them. To who they were gifted, by which of Holy Roman Empire rulers and what was the reason? What happened to them later?
Especially any informations about spear gifted to Gerard of Lorraine (I believe that's the "Gerhard of Alsace" mentioned in Polish sources).