So, I was rereading Edgedancer when I spotted several references to Lift's mother I missed the first time. I don't know if there's already another thread on this, but I couldn't find one. Anyway, here we go.
I think the loss of her mother and the subsequent things she went through as a result might be how Lift was "broken", allowing her to have the potential to form a Nahel bond.
There's this WoB that says that there was loss involved in her visit to the Nightwatcher.
From Chapter 5:
From Chapter 15:
From Chapter 17, where Lift is in a group of urchins:
From Chapters 10 and 17, where Wyndle asks why she acts the way she does, and Lift later responds:
And finally, the interlude in Words of Radiance:
I think that originally, Lift lived with her mother, who she describes as a kindly, loving person, and that Lift was happy during those early years. Then, her mother got sick, and Lift, for some reason, didn't take care of her properly (or at least she perceived it that way). Eventually, Lift's mother died, and she became a street urchin. At first, she struggled with surviving, but eventually got better at it. During this time, Lift started trying to distance herself from other people in an effort not to get attached, so that she wasn't responsible for their welfare and therefore couldn't be hurt if she let them down. Sometime during this period, she couldn't take doing the whole "being cold and uncaring and emotionless" thing full-scale anymore and visited the Nightwatcher, asking to have her aging stopped. I guess this was an excuse for her to continue to run around flippantly without caring too deeply for anybody (since theoretically, she could say that since she's eventually going to see them die or something, there's no point in developing a relationship).
I think her progression as a Radiant is supposed to help her learn to care again, kind of like how Kaladin's is about giving protecting another try.
If I missed anything, please let me know. Thanks!