Perhaps, but I know my quizzie would have looked into memories for several reasons.
- she would have wanted to know more about the orb that Corypheous had, if they had anything on that it might have led to Solas.
- She'd look back into Mythal to see if there's anything that will give her a better idea of what she got herself into
- She also would have looked back into 'the people' to understand why abelas called her a 'shem'.
- After hearing about Mythal's murder she also would have looked for things on that to see what actually happened, which would have led her to look into more about the gods/lore in general. (I was playing a very... "elfy" elf as Sera would put it.)
- If she had not looked more into the gods and lore due to reasons above she likely would have started looking into lore and history that is available after Solas tells her about the vallaslin.
If they knew who Solas was it seems likely to me that Lavellan would have eventually ran into something that made her question Solas. If she had not, she likely would have still found memories related enough to him that she would have brought up to Solas (even innocently not suspecting something strange about him) and his reactions could have warranted suspicion. My inquisitor also had a good relationship with Cole. Some of the things he may have said about Solas or with Solas while traveling (banters and whatnot) may have been enough to trigger her to question him.