When would you say your Lavellan started to suspect that Solas may not be exactly who he says he is.
I imagine that my Lavellan kind of knew something was off from the get go- but her first assumption was completely different from reality.
She is a very curious and overbearing person. She wouldn't have been satisfied with vague answers...but I don't think she would have necessarily pushed them, either. Elves have hard lives in Dragon Age. A lot can happen to them. I think her first feeling was that something rather awful had happened to Solas somewhere along the line, and that was what he didn't want to talk about. At first she probably thought shem were to blame. That he might have had a family at some point. But over time and hearing his ambivalence towards the Dalish, I think she came to the conclusion that he might have ran off from an alienage, attempted to join the Dalish, and was rejected. With some sort of trauma happening somewhere in between.
So she never really pushed it, thinking that he'd eventually tell her at some point.
It was only around the temple of Mythal that she actually started thinking about the ancient elves. Once she knew they were alive, then I think she determined pretty quickly that he was likely one of them. But then the drama between them went down, and Corypheus attacks shortly after- so she never quite got to get her proper confrontation.
Now that he's gone though, she's pretty certain that she was wrong to be so careless. She's worried, both for him, and for what she might have done by not pursuing the matter in her usual style.