Kehot does not sell a book of Kinnos for Tisha B'Av, and so this led me to assume there was no particular nusach that Lubavitchers use for kinnos. If that is so, what nusach is used? Nusach Ashkenaz? Some random Nusach Sfard version? I have not attended a Chabad house on Tisha B'Av so I really don't know what publication's generally used.
This article describing a publication of the prayers and laws for the entire Tisha B'Av according to the Chabad practice says:
הקינות נערכו על פי הנהוג בקהילות חב"ד, על פי נוסח האשכנזים
The Kinos are ordered according to what is customary in Chabad communities, [i.e.] according to the Nusach of Ashkenazim.
To the best of my knowledge, Chabad does not have a specific Nusach developed for Kinos, or any specific changes to Kinos. They do not say the additional ones printed in some versions that mention The Holocaust.