X-rated Bob wrote
Surely you'd want a lubricant that isn't going to be so sticky? Substances like vaseline are going to hold any grime and dust that they encounter. I'd think a dry lubricant such as graphite would do a better job.
Absolutely.
The Graph Tech String trees are the best (Teflon impregnated). I use staggered locking tuners, so string trees are not needed at all. In conjunction with a Graph Tech Black Tusq nuts, my guitars stay perfectly in tune all the time (until it's time to change strings).