I have arrived in Riften for the first time, met up with Mjoll the Lioness and Aerin her creepy boyfriend/stalker, and talked to her about all manner of things. She told me of her Dwemer Ruin exploration, how she lost her sword Grimsever, and how it was an emotional ordeal with long-lasting scars etc etc. But she will not offer me the option to recover the sword for her.

Do I have to do something to get her to do that? I have explored ALL dialogue options, and none give me any choices or anything to say. The first time I did this quest, I remember her giving me the option to retrieve it after I simply talked to her for the first time when I went to Riften on my Warrior.

you have to level up then talk to her again, that's what triggers the quest.

Also for future reference i recommend you search on uesp first

http://uesp.net/

I'm pretty sure that you need to be level 14 to receive the quest.

Level up and be sure to agree with her about the Thieves Guild.

I am level 29, and I have agreed with her about the Thieves Guild.

I've always gotten the quest to recover the sword the first time the subject comes up, I've never had to hear about it first and go away and come back. And that includes the time that our first meeting was me beating the crap out of her on a Companions job. I don't ever remember having to talk to her about the Thieves Guild at all, much less express a specific opinion about it. The subject may have come up since that seems to be her raison d'etre but not in a way that blocked or triggered the sword quest.

Level up and search on the Uesp...however,Myoll is useless in my opinion. and that guy Aerin is a coc*svcker

I love how people say "LOL LERN2 UESP" when I have stated my level and the fact that I have indeed talked to her about the Thieves Guild. Stop being ignorant and read. I have perused the UESP for half an hour to no avail.