The Evas do not intrinsically have souls,
but human souls reside within them.
They were all salvaged.
The only vessel that contained a soul was Rei.
She was the only one born with a soul.
The Chamber of Guf had been emptied, you see.
NGE2 CI wrote:1. The Development of Eva (Eva no Kouzou)
C. Confidential Information
An Eva is a vessel for a soul that has abandoned human form, and a
magnification of the ego, i.e., the embodiment of a large human being.
Rei is a vessel for a soul as are the Evas. She isn't talking about Lilim in any way. The Guf she speaks of must be Adam's since the Evas are created from Adam. Rei happens to be a fluke. She was only born with a soul because she sucked in Lilith's somehow. There was never suposed to be a Rei Ayanami, Yui was suposed to be reborn instead, so linking her to the Lilim is barking up the wrong tree.