Guide Mentor
Character Role Analysis
Leibowitz
Leibowitz is the guide or mentor character. That's a given. But… your precise interpretation of the novel will determine what type of guide or mentor character you think he is.
First, let's consider Leibowitz as the Obi-Wan Kenobi mentor. This immortal character pops up from time to time to offer members of the Leibowitz Abbey assistance or advice, and often in cryptic ways.
The old wanderer helps Francis find the Fallout Shelter. Benjamin offers Dom Paulo advice in the form of riddles. The old beggar hints that Zerchi's hopes for the future are already null and void.
Assuming these are all the same character—Leibowitz—then presto, we have an immortal guide. We have our Obi-Wan Kenobi, minus the ghostly special effects.
Now let's consider Leibowitz as a not-so-immortal mentor. In this scenario, Leibowitz is not Benjamin or any of the wanderer characters. He was martyred during the time of the Simplification, and stayed good and dead like any decent martyr would.
In this case, he's still the mentor because his teachings have directed the course of the abbey and its disciples for generations. This is best seen when Francis takes the vows of monkhood. He receives a bindlestiff, same as Leibowitz, and professes to be a booklegger and "'suffer death before betraying thy brethren'" (7.30).
In later eras, Dom Paulo and Zerchi are also be influenced by the story of Leibowitz in their respective conflicts. So, immortal or not, at least we know that Leibowitz is a mentor.