Ok, I've got this here theory on LTT and Rand and Moridin.
And you'll will most likely disagree with me here.
In ACoS, we see that Rand and Moridin have connected themsleves to each other with the use of balefire, and in KoD, this is further reinforced with one of Rands POV's. He describes the face he sees in his head; "...the face of the man from Shadar Logoth floated in his head for a moment. He looked furious. And near to sicking up. Without any doubt he was aware of Rand in that moment, and Rand of him. Move a hair in any direction, and they would touch. No more than a hair."
We see here, that Moridin and Rand have some sort of mental link, which when Rand reachs for saidin, Moridin's face pops up. The thing here is, Rand described that if he moved a hair, they would touch. This would imply that their minds would be open to each other. Now, my thoughts are, if their minds were completely open, would Lews Therin be able to transcend himself into Moridins mind? We know already, that Lews knows and acknowledges Moridin in Rands mind.
Now, when their minds are open to each other, Lews Therin is open to Moridin. Would it be possible to transfer Lews Therin to Moridins mind, and release saidin, closing the link. That way Rand can kill Moridin and give Lews Therin his peace. And Rand lives.
I know this theory isn't very concrete. But I do see that it is a plausible way to end the conflict of Lews Therin's death and Rand surviving.