Unfortunately, only one skin has its place in Genji's lore: Blackwatch (either the Young Genji or Sparrow skin is likely part of his lore too, though that is undetermined at present). Unlike League of Legends, for example, whose skin lines have their own universes and lore, Overwatch does nothing of the sort. At least, not yet. Aside from the few animated shorts and a couple of events (namely the Archive event), Overwatch didn't expand much on its lore. Hopefully, Overwatch 2 changes that.