One idea could be a crossover where Naruto, Sesshomaru, and a member of the Inuzuka clan are brought together by a powerful magic. They have to work together to defeat a common enemy that threatens all of their worlds. Naruto could use his Rasengan, Sesshomaru his Tenseiga, and the Inuzuka with their unique ninja dog techniques.
A mentor - student relationship could be explored. For example, Sesshomaru could be a reluctant mentor to an Inuzuka who has a lot to learn about controlling their inner beast, much like Sesshomaru has his own demonic powers to control. Naruto could also offer his own insights based on his experience with the Nine - Tails.
Sesshomaru would likely be aloof and haughty at first. He might look down on Naruto as a mere human. Naruto, being his friendly self, would probably be curious about Sesshomaru and try to start a conversation. Sesshomaru might respond with cold remarks, but Naruto's persistence could gradually break through his icy exterior.
Well, it depends on the specific fanfiction. Some fanfic writers like to create alternate universes where Naruto takes on different roles, and being the Inuzuka patriarch could be one of them. They might do this to explore how Naruto would interact with the Inuzuka clan's traditions and members in a whole new way.
One possible exploration in a Naruto and Tsume Inuzuka fanfiction could be their teamwork. They are both from the Hidden Leaf Village. Tsume is a strong and experienced ninja, while Naruto has his own unique abilities. In a fanfiction, they could go on a mission together that requires both of their skills, like infiltrating an enemy base. Naruto's ability to transform and his Rasengan could be combined with Tsume's Inuzuka clan techniques for a really exciting adventure.
One possible fanfiction could be about the Inuzuka Clan Head's journey to strengthen the clan's bond with other clans in the Hidden Leaf. He might face challenges like dealing with old rivalries and forging new alliances. For example, he could initiate a joint training program with the Aburame clan, which would be an interesting story arc as the two clans have different fighting styles.
Another theme is loyalty. The Inuzuka are known for their loyalty, and in fanfiction, this loyalty can be shown in different ways. Maybe an Inuzuka is loyal to Naruto no matter what, or they are loyal to their clan and Naruto helps them uphold that loyalty. It adds depth to the story.
One common theme is friendship. Since Naruto is all about making friends and the Inuzuka clan has its own tight - knit community, fanfictions often explore how Naruto forms bonds with the Inuzuka members. Another theme is power. Naruto's own power and how it might interact or be enhanced by the Inuzuka's unique abilities is often explored.
I'm not entirely sure which specific 'Naruto and Inuzuka Dogs' lemon fanfiction you're referring to. But generally, in Naruto, the Inuzuka clan and their dogs play important roles. A lemon fanfiction might explore relationships in a more romantic or even spicy way. However, it might also deviate from the original spirit of the Naruto series.
There are definitely some out there. I've seen ones where Naruto is put in a situation similar to Sesshomaru's, like having to deal with a powerful enemy or a complex moral dilemma in a way that Sesshomaru might. It's really interesting to see how authors blend the two very different universes of Naruto and Inuyasha (where Sesshomaru is from).