During the third millennium BC, a fragment of tablet of Tell Brak mentions the town of Lilabsinum among other towns that seem to be close to Nagar.
In the archives of Mari, it is probably the spelled city Nilibsinnu or Nilimmar. I4 is a tablet that informs of the capture of this city by Isme-Dagan, probably during the same campaign that targeted the Tell Shemsharah (Susarra). A.315 + mentions this city in the country of Kahat, threatened by the Turukkeans.
The archives of Tell Leilan evoke Nilibsinnum: L.87-394 and L.87-611 refer to information from Kahat about Nilibsinnum herdsmen whom Zurra men captured and attempted to sell as slaves. Probably Zurra designates a city that gave its name to the most eastern mountains of Sinjar, now the Djebel Ishkaft: Zara.
It is possible that Nilibsinnum is Nullu or Nulluenaswe - a place called "hamlet of the Lullubéans" – in the Nuzi archive.
This town is spelled Nilapsini when it was integrated into the Mitanni. At the time of Piyashili, son of Suppiluliuma in Karkemis, when the Hittites associated with the Mitanni confronted Assyria, the allies pursued the Assyrian troops in their retreat as far as Nilapsini, but failed to oblige them to battle.
All those mentions lead to consider that this city must be located between Tell Brak, Tell Leilan, Djebel Ishkaft and Yorgan Tepe.
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My notes of veracity :
Lilabsinum, Nilibsinnu, Nulluenaswe or Nilapsini, a same town at the east of Nagar and Subat-Enli: 3/5