At first, it could be a bit rocky. Bruce is used to his own way of doing things and Buffy has her own independent streak. But they would gradually learn to respect each other. Bruce might be impressed by Buffy's combat skills and her ability to handle the supernatural. Buffy, on the other hand, could learn a lot from Bruce's strategic thinking.
In this fanfic, Buffy might struggle with the expectations of being Bruce Wayne's daughter. She's used to her own world of slaying vampires and demons, but now she has to deal with the high - society life in Gotham. She could rebel against Bruce's over - protectiveness while still trying to uphold the family name in the public eye. Also, she might introduce some of her friends from Sunnydale to the Gotham scene, causing quite a stir.
One common theme could be the daughter's struggle with living in the shadow of her father's legacy. She might be trying to prove herself as a hero in her own right. Another theme could be family relationships. For example, how she interacts with Bruce Wayne as a father, dealing with his overprotectiveness or his high expectations. Also, the theme of identity might be present. Is she a vigilante like her father? Or does she choose a different path to make an impact in Gotham?
One great fanfic is 'The Father - Son Bond'. It beautifully explores the complex relationship between Bruce and Damian. It shows how Bruce tries to be a good father while also dealing with his role as Batman, and Damian's struggle to fit into this new world with his own strong - willed nature.
Another aspect could be that in some darker fanfics, if Bruce Wayne were to cross a moral line, perhaps Alfred would have to take more extreme measures. He might cut off Bruce's financial resources related to his vigilante activities. This would force Bruce to re - evaluate his actions and the way he operates as Batman. It's a way of punishing him to make him understand the importance of ethics even in his fight against crime.
He might develop a greater sense of humility. Without the Batman persona to fall back on, he has to face his own limitations as a person. For example, he may struggle to get people to listen to his ideas for change when he doesn't have the intimidation factor of Batman.
The plot is also important. It could involve them facing a new villain or a threat to Gotham that tests their relationship. Maybe a situation where Damian's actions put him at odds with Bruce's code of ethics, and they have to work through it. This kind of plot tension can make the fanfic really engaging.
I'm not sure if there is a specific 'Bruce Wayne lemon harem fanfic' available. There are countless fanfics out there, but a harem fanfic involving Bruce Wayne might not be as common as more traditional Batman - related fanfictions. You could try searching on specialized fanfic websites like Archive of Our Own or FanFiction.net.
A great idea for a Bruce Wayne training fanfic could be his training in stealth. He would practice moving silently through the shadows of Gotham. This could include training in different terrains, like the rooftops or the sewers.
In a fanfic, the family aspect could also include other characters. Maybe Bruce has a new family member that Terry has to protect, or there are family secrets that they both uncover. This could lead to a lot of drama and action. It could also show how Terry's own family views his role as Batman and how that affects his relationships at home.