I think you hit the nail in the head. Plus she is mortal.. like an ant or a butterfly, her life is to brief for an immortal to care about.. At least she thinks so
And maybe even Solas thinks like that. He knows he is going to lose her in "the blink of an eye" for him so he shuts her out of his life to give Lavellan a chance to find another chance at love with a mortal like her
Meanie egg elff 
Since it's brought up I think it's interesting to explore these immortal + mortal romances. I've only seen them dealt with a few times in media (I'm probably not as versed as I could be). The main thing that comes to mind is Highlander, and I haven't seen that movie in FOREVER so my memory of it is rusty at best. Oh, and Arwen and Aragorn in LOTR, though that one always confused me because Elrond always said she would lose her immortality if she stayed, and Aragorn was one of those humans that lived a really long time (like centuries) so how was this an issue? Eh, again, my memory's probably rusty.
But I feel like the immortal+mortal love is automatically doomed is so trite. I mean, yes, it is "doomed" in the sense that the mortal will die. But to deny yourself the pleasure of their company, however fleeting, how is that wrong or undesirable? It seems like the message is, I'd rather have the (smaller) pain of losing you now than the (larger) pain of losing you later. How would the pain be worse later? I feel like knowing you left your soul mate behind would be torture. Also, leaving them hurts them, whereas if you both live happily until they die, they get to live and die happy. It's not like you ever hurt them just by being immortal (other than maybe they are super jealous).
Besides, if you really are immortal among a land of mortals, you'd think you'd get a bit used to loss and be willing to risk it, since the gains you get of spending time with someone you truly love is worth it. As it's been pointed out, Solas probably likes Lavellan because of how unique she is. She's like nothing he's seen before. Why would you leave that? If you're immortal and almost nothing is new to you anymore, why would you leave the few things that remain?
Eh, I don't know. I guess I just have to say immortal/mortal romances have always left me with more questions than answers. They never seem very "realistic" to me, meaning thought out. It seems like people just think to themselves "Well he's going to live forever and she's not, why bother!" and call it a day. To me it's like saying if someone has a terminal illness and will die at 25, then they don't deserve to be loved, and whoever loves them should just cut their losses now and leave before you have to watch them die. And all I can think is...
what.
So in my mind I don't think Solas leaving Lavellan had anything to do with his immortality. I think it had much more to do with the whole "I have wrongs to right" part.
I also want to point out that in the DA universe, the whole immortal/mortal thing is rather ambiguous. Maybe someone knows more than I do from the codices, but the tales say the elves lost their immortality from contact with humans. So wouldn't this mean Solas could become mortal if he stayed? If that was what he wanted, it seems like he could.
I also have a suspicion the opposite could be true--that there is some way the elves could regain their lost immortality. So there could be that quest to do for Lavellan, like how the Warden is looking for a Blight cure.