Interesting post Hope,
Just a few additional facts hopefully of interest , the term 'Lullubi' or 'Lullu' appears to have been adopted as a generic Babylonian/Assyrian term for 'highlander', while the original region of Lullubi, to which it relates was also known as Zamua.
The Lullubi or Lulubi were a group of Pre-Iranian tribes who existed during the 3rd millennium BC, from a region known as Lulubum, now the Sharazor plain of the Zagros Mountains of modern Iraqi Kurdistan.
Lullubum in ancient times is alluded to as one of the territories subjugated by Sargon the Great (hints of 'Lord of the Rings') then absorbed into his Akkadian Empire, along with the neighbouring province of Gutium, probably of the same origin as the Lullubi.
Following the eventual fall of the Akkadian Empire to the Gutians, the Lullubians then rebelled against the Gutian King Erridupizir, according to inscriptions relating this specific pre-second millennium BC monarch.
Following the Gutian period, the Neo-Sumerian (Ur-III) ruler Shulgi allegedly raided Lullubi at least 9 times; during the rule of Amar-Sin, Lullubians formed a contingent within the military of Ur, suggesting that the region was by then under Neo-Sumerian control.
Akkadian Stele of Naram Suen 2120 BC relating to Lullabi and Zagros Mountains