Regarding the Dragon and the Dragon Reborn (and Graendal’s thoughts about Ishamael’s musings):
“Is this soul born in any other Age, or only at the advent and (theoretically, of course) the closing of the Third Age, as the Dragon/the Dragon Reborn?”
This soul is one of the Heroes, and bound to the Wheel, spun out as the Pattern wills. “It” is born in other Ages, but in a non-Dragon incarnation, to suit the pattern of that Age.
In the course of this answer, he related this to why Hawkwing calls Rand “Lews Therin” at Falme—because Hawkwing recognizes this soul. This didn’t really tell me why he specifically calls him “Lews Therin”, but apparently they’ve been hangin’ together in Tel’aran’rhiod and the etiquette there is to call each other by the name of your last incarnation. (My interpretation.)
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