Might i suggest that her story was true and false?
All the events she described did take place in Ferelden, but she went with Dorothea to Orlais and got arrested for treason, because of Marjolaine using her own talents, to make her an enemy of Orlais stopping her from ever being a threat. Orlais doesn't like traitors after all and for someone like Marjolaine doing so would be easy for her after all she taught Liliana everything she knows about being a Bard.
Now Dorothea either saw or learned of this, and went to work helping her escape, maybe even using her influence with the Divine to make Liliana a Seeker of Truth. But because of all the dangers she told Liliana to return to Lothering to escape the dangers that were present in Orlais, until such a time either she or Dorothea could remove the threats towards her. This would place her in Lothering, the place where she either met Dorothea or the Chantry Dorothea started in, or maybe even just the safest place Dorothea could think of considering how mundane a place Lothering is. Heck even the Hawke's used it to that advantage. Its so plain no-one thinks Apostates could be their neighbor. So at the very least it seemed Liliana was safe there.
Now her joining the Wardens is sincere. She tells her story with a half truth as a way to protect herself. She may be a generally nice person, but if she's too trusting she could end up in danger. She trusted Marjolaine after all, and if the Warden fulfilled poisoned the Urn, then they nearly killed her, forcing her to drag herself off a mountain towards civilization that would help her, while a Blight was going on, so all in all she has very good reason to twist the truth. After all the events in Dragon Age 2 span about 7 years, in game, and we encounter Liliana in Act 3 of the story.
All in all its safe to say that Liliana isn't an agent or the Left Hand of the Divine at the time of Dragon Age: Origins. Its more than likely she became such after the Archdemon was defeated.
That's my theory anyway.
Though from a development standpoint, her being an agent of the divine in any way shape or form, probably wasn't even a consideration back then. If they ever go back and re-release the Dragon Age series years from now, and update everything to be more Chronologically sound, then they might change certain things involving her to make it so she is undercover but that would seem like a lot of work on their part. The most i think they'd do is edit her story in Dragon Age: Origins to match that of Liliana's Song, other than that I think its just a sign of how much the original idea of Dragon Age has evolved. I'd even bet they wish an Age in the Dragon Age Universe lasted more than a 100 years, because in a way it could limit what they do. A game called Dragon Age based in the Chantry Age isn't likely to sound good when the previous years were in the Dragon Age. Makes things rather confusing.
But on your suggestion of the Guardian knowing about Flemeth and what she really is...questionable. From a development standpoint Morrigans response to the Guardian just matches her personality and the line add more mystery to her deepest secrets. So its more than likely the development team just adding more emphasis to her personality, like how she's immune to the Sloth Demon in the Circle of Magi. It might just be adding to the display of her magical prowess. but story wise I personally doubt it.
The Guardian is asking people things that tests the fibre of who they are. Zevran an Assassin by trade who enjoys his work, still regrets one kill above all else, Stens only guilt is his murder of the farmer and his family, and Liliana's only solace in her what was becoming a mundane plain life, with none of the excitement she loved when playing her little court game, was forced to question her own ideas. The Guardian would more than likely state a fact in such a way that it would have made Morrigan question herself, and that is something she will not allow. So her dismissal isn't some secret she wishes to keep, but her own confidence in who she is.