Actually, neither seem to fit. Why? Because Rand says it's odd it's from his own memory, not Lews Therin's. So, there's something bizarre going on. This is emphasized by the fact Rand points he told no one, not even Min about it. The events out of the Waste shown in Rhuidean are not centuries old, they occured centuries after the Breaking. This doesn't fit.

It seems obvious the scabbard/sword was found near the manor, by the Asha'man digging. They found that recently, brought it to Rand.

Who could have lost a sword with dragons in this area of the Westlands, centuries ago? Elementary, Dr. Watson. It's Guaire Amalasan. Hawkwing fought him in that area, this area is part of Amalasan's first conquests. Rand, in a struggle against Tuon, just got the sword of Hawkwing's archefoe.

But how the heck can Rand know this?

>Rand's head is getting invaded by new people - perhaps the barrier is completely broken and gradually new dead people he isn't the rebirth of will do 'walk-ins'. Not impossible, but a bit loony

>Moridin. Technically, Ishamael shouldn't have been around yet by the time of Amalasan - he joined Hawkwing's court decades later, after the Consolidation. Moridin may however well know enough about those times to know Amalasan had a scabbard like this (which he may have lost and got replaced by another just like it, obviously). This Sword may be as famous as Hawkwing's own Justice. So, it's not Rand but maybe Moridin who knows what this sword is.

> A more puzzling idea: another who could very well remember this sword (even if I'm wrong it's Amalasan, but I'm pretty sure I'm not) is Mat. Rand may be beginning to access Mat's 'Finn' memories at random, without even realizing it's not his own. We may be seing a new incremenent in the 'colours' phenomenon. Eh, eh... if that is so, Rand may be starting to hear wolves next. LOL! I laugh, but if this is what it is, this is rapidly going to escalate into a big tangle. Rand would see Tuon and think of her as his wife and all that sort of thing. You know, I think this one might be my favourite of the three ideas, as loony as it sounds.