It is possible, as Amalasan assieged the Stone of Tear too.

It's just surprising Brandon didn't opt for :

"He had recognized the weapon from a description in a book he has read in Tear."

It's really bizarre that he rather chose to go with a wording that make the reader expect knows the weapon from his own memories. It's not the weapon he has memories about, it's memories have read about it in a book. This doesn't explain the 'oddly' bit either.

I've had more time to think about it, and refined the ideas a bit (and Linda pointed out I gave the word unearthed the sense we normally use the equivalent word in French, to dig up the ground, not the more figurative meaning of to discover). So... now I think it's more likely people, Domani dragonsworn maybe, came to give Rand this sword earlier on - a gift that seemed fitting for him - with the Dragons on it and all, though they didn't know what this weapon is, but it was discovered recently (or so they think.)

There's supposed to be a 'small scene' in the prologue connected to that chapter. At first I thought it could be a short Semirhage POV with Cadsuane/Nynaeve.

The snippet about the sword is really 'mysterious' but it's not written well to be a mystery (not as if this is supposed to be a mystery to unveil later, I mean - only the last sentence about 'Oddly, this didn't came from LTT's memories but his own", and I'm wondering a lot if that's not simply because we're supposed to know what this sword is all about, if the only intended mystery is not the bit that Rand knows what this weapon is, from his own memories.

So I'm wondering now if the short scene in the prologue doesn't simply happen a while before, and doesn't involve people who decide to bring this sword to Rand. I also factored in a few more elements from the chapter and worked them backward, for fun. I came up with this:

- The short scene in the prologue is a Graendal POV. She is musing about the sword, which has secretely been the possession of the Domani royals (or Alsalam's House), which they hid from the Tower, for obvious reasons, because it is believed to have belonged to Guaire Amalasan. She has taken it from Alsalam. She is amused that the sword is Amalasan, because she very much hopes (or has been ordered to make sure) Rand will turn against the Seanchan. What irony, this sword from Hawkwing's own archfoe? Then Graendal goes on and solves the problem that Rand may be implying that LTT too may have recognized the sword/scabbard from memory: the scabbard is amusing her, because it is obviously intended to be a replica of Lews Therin's own from the War of Shadow. As if Amalasan had read a description of it and had it made. "Al'thor was mad, on the brink of terminal madness. She would very much like to study him - such a break-through case. In her own age, there had been theories that the inner voices heard by some mad persons could be real, voices from their past lives seeping through. But this was never proven as no one ever found a way to establish who someone had been in a past life. But Al'Thor had been Lews Therin, and this explained his suprising skills, evidence he knows more than even Asmodean could ever teach him. And this means a simple few pushes and pulls and she would have him fall into the terminal madness Moridin wanted. Her arrangements with him to manipulate the others had paid dividends, and she would find a way to exploit his madness too, and make him fall before the end. But now, it was time to make her opening move with al'Thor".

She weaves her Basene Illusion, meets a few Domani dragonsworm and tells them this sword has recently been discovered, she doesn't know what it is but she wants it to be a gift to the Dragon Reborn from his most loyal supporter, the Lady Basene.

This covers pretty much all angles, I think. The matter of the memory is the mystery that will resurface later in the book. LTT could have recognized it (and MAY have - nothing yet fully excludes the possibility Rand didn't mean he recognized the sword from his own memory, later LTT did too) as a replica of his own sword, but mysteriously it's Rand who recognized it as Amalasan's sword, a few centuries old (not millenia, this can't be LTT's weapon - not even something Rand saw in the Glass Columns, pre founding of Rhuidean), given to him by Domani nobles, emissaries from Basene who sent him the gift, and who didn't know what it was.

I think this also fits perfectly with the sort of mind games Graendal likes to play.

This would explain why Rand implies the sword wasn't made for the Dragon (reborn or not, IMO) but seems to have been made for him, and the comment that it's so very odd this sword is unearthed now, and given to him, can be explained in two ways:

- Rand means it's odd he is given this sword now, when his secret that he 'hosts' Lews Therin has just come out, and TG is coming.

- Rand is thinking of the Amalasan-Hawkwing stories, and the fact he is sent this sword, right as he faces Hawkwing's heir.

The fact Graendal sent the sword on purpose, as a mind game, explains 'odd' too, as Rand is right, it seems like an awful coincidence.

While we're on it, Rand's reflections about Asmodean knowing Graendal's location, and remembering he vanished etc. and his reflections about stepping wearily and be careful of Graendal becomes far more interesting if this isn't foreshadowing (if it is, it is clumsy to rbing back the main clue from TFOH as is and so bluntly) but rather an RJ-style reaction-with-missing-information to the earlier POV. First, Rand is worrying about Graendal without knowing she's already after him, and secondly during the Graendal POV she may muse something like:

"It had taken a very long time for al'Thor to finally come time way. Longer than she had feared once. The day he had killed Lanfear and Rahvin, she had thought she would have to leave this palace and her pleasures, that he would come after her like a pointed arrow. She had received Asmodean in this very room once - she had expected him to betray her to al'Thor - she had known she would have to take care of this, if the plan in Illian didn't work. This delay, this chance to focus his attention on Sammael instead of her, had been the reason she had agreed to be part of that plan.

She could not but smile at the irony that it was Asmodean and not her who had died that day. She had come to the palace in Caemlyn to investigate after Rahvin failed to meet her that day as agreed. Asmodean had surprised as she was busy compelling spies among the servants that would report to her what al'Thor planned next. She had balefired him, a very short amount - she could not afford to remove more than seconds from the thread of anyone who had passed that door, could not know what the person had been doing minutes ago. She had fled and waited. The great Lord had made been pleased with her report that she had eliminated the traitor. He all but made her promises that day. And Al'Thor never came - foolish of him if he hesitated because she was a woman. Now she was ready for him, and he would fall in her snares."

Another possibility, slim I guess, is that the scabbard is a fake. Graendal is quite the forger. She may have picked an old collectible from Alsalam or whoever, and forge the decorations to get a replica of LTT's sword. Investigating old stories about Hawkwing etc., she had learned Guaire Amalasan had such a replica.