I love this whole conversation! I'd like to add a few edgedancer traits:
1. There is the scene from WoR where Adolin gives his helmet to the water boy and shallan mentions how nice he is to everyone. I think that fits the edgedancer stereotype of being the ones caring for the simple people.
2. Adolin seems to be the only one who used to really listen to Renarin who was never heard by others.
3. Adolin tells shallan off for not taking care of her bodyguards which shows that he cares for them.
4. It was said before but he remembers the forgotten horse of Dalinar.
Of those, 1, 2 & 4 are examples I could very well imagine Lift doing as well.
On a side note I think that Adolin could be an elegant addition to the battlefield sliding around well dressed, striking with perfection, etc. I could also see him teaching sword stances to Lift. And I can already hear Wyndle's mutterings on the elegance of Adolin and how he ended up with Lift instead