Speaking off. Wouldn't it be possible for the inquisitor to find Solas again in the fade? Or would he have some sort of defence mechanism to prevent her seeking him out even in their dreams.
Since he can apparently erase Cole's memory of talking to him during the post credits scene and keep him from his mind I imagine he can keep Lavellan from finding him in his dreams.
I actually tried to figure this out shortly after finishing my first PT. First, she'd have to be a mage in order to enter the Fade without using the mark, while lucid (i.e. not just while she's dreaming). I think that Lavellan cannot manipulate the Fade while there physically, if she can even do it while she's dreaming or while there in a lucid state. The game isn't really clear on this and there's some conflicting information on the wiki. Anyway, to get into the Fade while lucid she'd need a significant amount of lyrium, and/or blood magic, and/or other magics. Then there are two choices. According to the wiki, one can use blood magic to find someone if they are asleep, but only if they do not have some sort of defense against blood magic. We have no idea if Solas does, but the answer is probably yes. The second choice is to try and bargain with a spirit/demon to find him. Which runs the risk of possession. So....you're either dealing with blood magic that may or may not work, or you're opening yourself up to being a demon-host and can you imagine how horrible a demon possessing the body of someone with the Anchor would be? (If Lavellan happened to have a phylactery of Solas' blood she could use that pretty easily though)
My headcanon is that she finds a spirit of Purpose and gives it a mission to go find the dumbo to deliver a message. She knows that Solas has a soft spot for spirits and won't deny Purpose its, well, purpose, even if he wants to disappear without a trace. She only does it once, to let him know that he doesn't have to be alone, but I like that he can't just be all kkthxbai with no repercussions the jerk.