The doorway was in a AS-founded city (rhuidean), so the AoL folks would've known something about it and studied it. Although you say Lanfear might not have specialized in it, I doubt she'd be clueless in 'Finnland. Lanfear knew about the Portal Stones, didn't she? Knew them well enough to critique Rand's use of it and comfortably hop between universes without a care in the world. So Lanfear is familiar with ancient dimensional oddities...

Moiraine & Rand said the Snakes speak an odd dialect of Old Tongue, and Matt comprehended both. This means Lanfear would prolly understand the Foxes perfectly. Current Randland folks play that S&F game, which is quite old, so there's good odds she's heard the chant before.

Lanfear isn't a trusting person, so she'd never ask a bunch of weirdos for stuff without thinking about possible costs; Mat makes that mistake because he's reckless and ignorant. Lanfear's only big-time stupid when it involves LTT (I think).

Given her new OT name, I think Lanfear was killed - either because of the doorway or by the Dark on her return. Her reduced power level suggests she: (a) was burnt out and healed by a woman or (b) sacrificed some power (oh the irony) in a deal with the foxes.

One final note that I (sincerely) hope doesn't sound nitpicky: I doubt Lanfear thought that Rand was much stronger than she expected. She kicked his ass, making him and the girls suffer, and all he did was cry & laugh. If you wrote this to provide extra motivation, she didn't need it. After all, she nearly killed Asmo when all he did was back out on their deal and use her old name! Rand sees raw fury on her face and must *remind her* that they both want Asmo teaching the Dragon. She seriously had that evil Liberace's number.

I've often considered that Mierin/Lanfear/Cyndane (aka MiLaCyn) might've killed Asmo - she has genuine motive for it, can prolly kill so resurrection is impossible, & is one of 2-3 folks who swore to kill him on sight. I think your idea needs work, but encourage you to keep trying.