Laziridis 2016 :

Extreme regional differentiation in the ancient Near East
PCA on present-day West Eurasian populations (Methods)(Extended Data Fig. 1) on which we projected the ancient individuals(Fig. 1b) replicates previous findings of a Europe-Near Eastcontrast along the horizontal Principal Component 1 (PC1) and parallelclines (PC2) in both Europe and the Near East (Extended DataFig. 1)7,8,13. Ancient samples from the Levant project at one end of theNear Eastern cline, and ancient samples from Iran at the other. Thetwo Caucasus Hunter Gatherers (CHG)9 are less extreme along PC1than the Mesolithic and Neolithic individuals from Iran, while individualsfrom Chalcolithic Anatolia, Iran, and Armenia, and BronzeAge Armenia occupy intermediate positions.

(I don't have the actual PCA chart in good resolution)

So Iran neo is further away from Levant than CHG.
CHG was there long time and probably there was some limited contact with the Levant.
What must have happened is that some other folks came in prior to the Iran neo.
These other folks didn't have any contacts with the Levant, they probably came from north or east.
Who could they be?
Haplogroup R2 has been identified amongst Iran neolithic.