I'm curious to hear what a man claimed to have died and later risen encountered, as others are I'm sure. I've yet to come across any actual writing regarding this, especially outside of the Bible, so any answers are welcome!
No, there are no documents from Lazarus. Not even 2nd century pseudepigraphical writings claiming to be from Lazarus, which is surprising, since it would be quite normal for a 2nd century apocryphal text to assert something about him, but I am drawing a blank.
Sorry for a short, negative answer, but there is no document to talk about.
No, I doubt there is any historian (and hardly any Bible scholar) who thinks Lazarus was a historical individual.
The Gospel of John is a theological literary work, not a historical one. The story of Lazarus might be the author's way of refuting the Gospel of Luke, which also has a character named Lazarus in the Parable of the Rich Man and Lazarus. In Luke's story, Lazarus dies, and the rich man begs that Lazarus be raised from the dead as a sign so that people will repent. However, he is told that even given such signs, people will not repent. In John's story, contrary to Luke, Lazarus does indeed rise from the dead, and his resurrection convinces many people to follow Jesus.
To put your question in a larger context, we have no documented testimony or evidence even for Jesus or the events of the Gospels from any contemporary writer. The Gospels themselves are anonymous and were written quite some time after the events they portray.