Well, one possibility is that Aang's friends could find a way to heal him. Maybe Katara would use her waterbending skills in a new and innovative way to reverse the damage caused by the lightning. Another idea is that Aang could enter a spiritual realm while in this injured state and gain new insights or powers that would help him when he recovers.
The impact on the plot could also be emotional. Aang being shot by lightning would be a huge shock to his friends. This could lead to moments of self - doubt among them. For instance, Katara might blame herself for not being able to protect Aang. Sokka might question their ability to continue their journey without a fully functional Avatar. These emotional upheavals could add depth to the characters and drive the plot in new directions as they struggle to overcome their internal and external challenges.
He could meet his future self. It would be an interesting encounter as he could learn from his future experiences and wisdom. Or he might meet people who have studied his past adventures and see himself through their eyes.
Possibly they are random villagers who were caught in the crossfire of a conflict between different bending factions. Aang, being the Avatar and a symbol of peace, feels responsible for burying them and ensuring their spirits are at peace.
He might start by observing. Aang is a curious person, so he'd likely watch how people live, how they interact with technology. He may also try to find other benders to learn about any new developments in bending. And he'd probably use his kind heart to make friends easily in this new future environment.
Sokka could be one of the main characters. He might be the one helping Aang with his schoolwork, especially in subjects like history or math, using his own knowledge and quick thinking.
Aang might go into a deep state of depression. He has always been an emotional character, and having his heart broken by Katara, someone he loves deeply, could send him into a downward spiral. He might isolate himself from his friends and stop practicing his bending for a while.
In some fanfictions, Aang's connection to his past lives plays a crucial role. He could draw on the wisdom and skills of previous Avatars. They might guide him on how to defeat Azula specifically. He could learn a new bending technique from one of his past lives that gives him an edge over Azula's firebending, like a unique way of using water to extinguish her most powerful fire blasts.
Well, Aang being the Avatar has a deep connection with the elements. In this fanfiction, perhaps he enters the Avatar State and uses all his elemental powers in harmony. He could use waterbending to create moisture and cool the volcano, combined with his airbending to disperse the heat and gases.