One of the popular characters paired with Sarutobi is Jiraiya. They are both important figures in the Hidden Leaf and their relationship, whether it's as comrades or as teacher - student in some fanfic interpretations, is always interesting to explore.
Perhaps in this fanfiction, Sarutobi is trapped in a genjutsu created by a rogue ninja. Naruto, being highly resistant to genjutsu due to his Uzumaki blood, manages to break into the genjutsu world. There, he has to fight his own inner demons as well as the rogue ninja's illusions to free Sarutobi.
Perhaps he uses some ninja techniques like a shadow clone jutsu. He could make multiple clones to help him sort through and complete the paperwork quickly.
I really like 'Naruto, Sasuke and Sarutobi: A New Beginning'. In this fanfic, it starts with Sarutobi having a premonition about the future of Naruto and Sasuke. So he takes steps to guide them differently. It's an interesting take on their relationship. 'Sasuke's Redemption under Sarutobi' is also good. It shows Sasuke trying to make amends with the village with Sarutobi's guiding spirit in mind. And 'The Hidden Power of the Trio' is a fanfic that gives a new perspective on the powers they possess and how they can be combined for the greater good.
In this type of fanfiction, it's possible that the story delves into Naruto's backstory and how being Sarutobi's son would have affected his childhood. Maybe he would have grown up with more guidance and support, which could have changed his personality. Instead of being the lonely outcast that he was in the original story, he could have been more confident from the start. The fanfiction might also introduce new characters related to Sarutobi that play important roles in Naruto's life. There could be new adventures and challenges that are unique to this new family dynamic, such as Naruto having to uphold the Sarutobi family name and legacy within the Hidden Leaf Village.
Naruto would probably be extremely hurt. He has always looked up to Sarutobi as a leader and a father figure. His first reaction might be disbelief, unable to accept that Sarutobi would do such a thing. Then he would likely feel a great sense of anger and betrayal. He might lash out and try to prove his innocence.
I'm not sure about a specific 'Naruto Mirai Sarutobi Lemon Fanfiction' to recommend. Fanfictions can vary greatly in quality and content. You might want to check popular fanfiction websites like Fanfiction.net or Archive of Our Own and search for it there, then read the reviews to find a well - liked one.
In the fanfiction, Sarutobi could be kidnapped by a group of ninjas from another village. Naruto would then embark on a solo mission to rescue him. He'd use his stealth skills and knowledge of the terrain to infiltrate the enemy's hideout and save Sarutobi without being detected.
A common theme is the exploration of Ayame's character. Fanfics often delve into who she really is beyond her role as a ramen shop owner. They might show her hidden skills or her dreams and how Naruto fits into all of that. Community and family are also themes. The fanfics might show how their relationship affects the wider community in the village or how it relates to their own ideas of family.