My script also follows differently with how he departed in their third romance scene. I see it as Solas (pride, solace, alone) wanting to fix what he perceives as a mistake (i'm thinking waking the Old Gods will result in more bloodshed and stripped freedom), which he caused in the first place. Since he was the one to cause it, he thinks "i should be the one to make it better" type deal. It's a duty and a responsibility, and there's a probability of it pitting him against all the people she loves.
Separation will make fulfilling his task easier, because she, and her beliefs, makes him doubt. Doubt doesn't fit into the equation of "fixing" the world on his own. It skews it, in fact. Malfunction must not happen. Plan must be enacted. Give the improbability the boot before it can cause harm. Like how Corephy-spit intended to kill the Inquisitor, despite being an unknown rival. Ending the relationship fits his big picture. It's a path he chooses to walk alone, even if it hurts. He's worn but accustomed to enduring.
Pride is still Solas' folly. He thinks he can do it alone, but he can't, really. Releasing the Old Gods may alleviate his guilt, or provoke further guilt of yet another mistake (which would be releasing havoc on Thedas, should the gods just happen to be angry

).
It parallels with Cassandra and the Seekers, in a way. Difference is that Cassandra acknowledged needing help and chose not to walk her path alone, because what she was doing was larger than her, no matter her capability or wish to carry out a one-man-lead crusade.
Now, I do 100% agree with you on Lavellan's naivety. There are so many red flags surrounding Solas--one neatly erect on his bald head, a couple coming out of his ears, one on this nose... just all over. It's frustrating, too, how little elvish she knows. My Lavellan definitely has emotional intelligence, but she is also an inquisitive and intellectual being, although those are subtle and overshadowed by her compassion. It's a shame she doesn't get to explore thought more, or ask provoking questions to surprise Solas even further.
alas, now I'm going to make an air-headed, domineering Andrastian human who discriminates against all races, was cloistered as a child, demands for attention, wouldn't know the word "modesty" if it was branded onto his (i will be making an egotistical, testosterone-driven male, yes) spanking-ass butt cheek... yet still leads a powerful movement.

i'm interested in how the inner circle will react in comparison to my humble, unassuming, knowledge-seeking, assertive, and sweeter-than-frilly cakes fem!Dalish.