People were talking about backgrounds earlier, so I thought I'd drop mine. I'm not a lavellan obviously, though I promise I'll make one!
But I still like Solas a lot, and he fits in very well with my character's story due to his background:
He always had a scholarly interest in the elves due to being bored with his life as a noble, and he tried getting close to the dalish clan lavellan, but at most could only establish a trade agreement with one hunter for lyrium that wasn't his. So when Solas comes in and drops him with this big trunk load of elven knowledge that even the dalish don't know, his inner nerd sort of sealed the bromance with him and Solas. He feeds his craving for knowledge, saved his life and dropped a castle on his lap when all seemed hopeless. Solas is my Merlin.
And now I'm always having him take the dip into the well, for curiousity, distrust in Morrigan's motives, and a desire to use it to help the Dalish and learn more. I honestly don't feel as though Morrigan would help the elves, I think she's more interested in the well for her own selfish curiousities more than anything. I decided finally that I'd make Cass Divine, so if she does end up breaking up with you, it'll give my Trev a chance to go and help the elven people like he said he would, and also maybe find his past love, since they were separated by Templars.
With everything that's happened to him, I'd imagine that he thinks his interest in elves was destined by the maker. He is andrastian, but to him the existance of elven gods only brings him closer to the truth about the maker, so he feels obligated to pursue his interest.