Vasher is such a fascinating character. If we look at his history, he's not really a good guy. He killed both Shashara and Arsteel, even when those deaths weren't necessary, he started the Manywar, his experiments with Investiture created one of the most dangerous weapons in the Cosmere.
And yet, there is one aspect of his character that has always been good: he's a great mentor. Somehow, despite all of his mistakes, every single person mentored by Vasher has ended up better because of it.
Vivenna is the one we see less of. But we know from Oathbringer that she became a talented swordswoman, a very capable leader and she might have been able to create an awakened sword like Nightblood that doesn't have the *issues* that Nightblood has.
Adolin is the best swordsman in the Stormlight Archive series and he was trained by Vasher. In many of Adolin's most important duels we see him remember Vasher's teachings. Even during the big duel scene in Words of Radiance, Vasher is trying to help him as he watches Adolin's struggle. Adolin goes out of his way to wait until Vasher is available to train Renarin because he knew that Renarin would be better off with him as a teacher (and he was right, Vasher never judges Renarin for his lack of physical abilities and in fact praises him for not questioning his teachings even when they seem silly).
Kaladin spent less time being mentored by Vasher, but somehow all of Vasher's teachings and advice were crutial for Kaladin's journey. One of my absolute favourite moments in Words of Radiance is when Kaladin asks him for advice to choose between two bad options and Vasher tells him to pick the one that makes it easier for Kaladin to sleep at night aka the one that will give him less regrets in the future. Without knowing Kaladin had asked the perfect man this question because Vasher is a man that has nothing but regrets. Vasher's words come back to Kaladin when he decided that siding with Moash was wrong and chooses to keep his promise to Dalinar. Then in Rhythm of War he doesn't let Kaladin join the Ardents because he knew it would be a mistake and that Kaladin didn't really wish for that, he was just lost at that time. I also find it interesting that Vasher is the one to teach Kaladin about Cognitive Shadows (and how over time they become less people and more their Intent) because Kaladin then chooses to become one by the end of Wind and Truth.
I wasn't that surprised that he asked Lift to mentor her. Vasher still doesn't know why Endowment had him Return, and he has certainly done a lot of terrible things with his extended life. But I think Vasher likes teaching, he likes that his long life has given him the experience that allows him to help others be better and not make the same mistakes he did. This probably is the closest thing to a purpose that he has (other than being an Investiture nerd, of course). So I think Lift will be all right. Maybe something will go down between them before or during Stormlight 6, but I am positive she will have much more control over her powers and have knowledge that will be important for her future.