Power is a major theme. Harry being in a position of power as Lord Azkaban has to learn how to use it responsibly. Another theme could be redemption, as he might try to redeem the prisoners or himself in some way.
The themes in 'Harry is Lord Azkaban' fanfiction are quite diverse. There's the theme of leadership, as Harry has to lead the inmates and the prison staff. Another is the exploration of the dark side of the wizarding world. Since Azkaban is a place full of dark magic and dark wizards, Harry has to face this darkness head - on. And finally, there's the theme of friendship. Even in a place like Azkaban, Harry might find some unexpected allies and form new friendships, which is an important aspect of his journey in this fanfiction.
Dumbledore might play an important role as well. He would be guiding Harry through this new and strange situation. He could have some secrets about the Lord of Azkaban that he reveals to Harry over time. Also, some of the Azkaban guards or prisoners could become significant characters as Harry tries to reshape Azkaban.
One interesting plot could be a new adventure where Harry discovers a hidden chamber in Azkaban that holds a powerful magical artifact. This artifact might be related to an ancient wizarding family and its secrets. Another plot could involve the Dementors having a different origin than what is known in the original series, and Harry has to find a way to stop them from spreading a new kind of dark magic.
One popular 'Harry is Lord Azkaban' fanfiction might be 'The Ascent of Harry in Azkaban'. It has an interesting take on how Harry gains power and influence within the prison. The story is full of mystery and unexpected plot twists.
It could be Harry Potter himself, of course. He might be on a mission to either free someone wrongly imprisoned in Caer Azkaban or to stop a new dark threat emerging from there. Hermione could also be a main character, using her intelligence to figure out the mysteries of Caer Azkaban.
In this fanfiction, perhaps a major plot point is Harry using his new position to reform Azkaban. He could introduce new ways of dealing with prisoners that are more humane. Also, his power might attract the attention of dark forces who want to either use him or destroy him, which would add a lot of action and suspense to the story.
Harry Potter himself is of course very common. He's usually the central figure in these fanfictions. Hermione Granger is also often included as she is Harry's friend and a brilliant witch. Ron Weasley too, as he's part of the trio. Sirius Black might also be a common character since he has a connection to Azkaban.
The Dementors could be the main antagonists. They are always a threat in Azkaban, sucking out the souls and happiness of the prisoners. They would be constantly trying to get at Harry and Daphne.
Obviously, Harry Potter is the central character. He's the one who is wrongly imprisoned in Azkaban.
It could be the corrupt prison guards or wardens. They might be in league with dark forces outside Azkaban. They oppose Harry and Ginny because the couple is getting too close to uncovering their illegal activities within the prison, like smuggling dark artifacts or collaborating with Death Eaters.
In the fanfic, there might be changes in the security measures of Azkaban. For example, new spells or wards could be added to prevent prisoners from escaping more effectively.