Scratchpad

Keep in mind two facts:
-Rand is stubborn as a mule. Once he had made a decision you can talk till the sun burns out and he'd not move an inch, regardless of logic or motivations, short of breaking him.
-Rand has a large number of people he routinely ignores, like Moiraine, Lanfear, Egwene, Nyneave, 95% of the nobility, etc...they never seem to realize that they're only training him to ignore them by persisting in an argument after he made a decision.

Lets not join them on the list.

[X] [B]Accept Rand's refusal and figure out another way to deal with Lanfear.[/B]
-[X] Work with Moiraine to come up with an alternative solution for Lanfear or any other Forsaken popping in. You can locate them extremely quickly, even if they show up by Traveling, but you can't land the killing blow. Moiraine can, so discuss arranging insect signals by which you could call for such a strike in an emergency on short notice.