Presumably, Lanfear had three wishes available when visiting the Aelfinn (or is it the Eelfinn?). You know, the foxes. No one had been there for the longest time. "The longest time" said the fox, echoing Mat's thoughts (I'm referring to the only time we've ever seen the foxes and their musk-smelling lair, in The Shadow Rising).

It's not even clear that, in the Age of Legends, the protocols were understood by everyone, or that Mierin would have gone through the portal (or that people were permitted to use them generally). I'm of the opinion that, given the danger, only specific scholars focused on the Finns would have gone through the portals, and Mierin was studying other things (like Shaitan's prison).

Given this knowledge (and the way Mat stumbled into his wishes), I think it's easy to reconstruct what happened:

Lanfear has just fallen through the ter'angreal. She's just confronted Rand and realized that he is a lot more powerful than she thought he would be. He is a lot more powerful than he SHOULD be, given how she instructed Asmodean. She thinks he betrayed her.

She ends up in the room with the foxes, just like Mat did in The Shadow Rising. Like Mat, she doesn't understand what they're saying about honoring the ancient agreement and what they mean when they ask what she needs.

"I could just kill Asmodean!" she shrieks.

"Done".

She appears in Caemlyn, balefires Asmodean and returns. This is probably said before Moiraine can do anything. With an evil glint in her eye she decides to do something awful to Moiraine as her second wish.

"Done".

Her third wish is probably something silly and stupid, like "I want to look like Ilyena so Lews Therin will remember me and fall in love with me."

"Done."

Ah...but she didn't discuss payment, did she?