Well, it could be that Hermione accidentally drinks a love potion during the Goblet of Fire events. Harry is the only one who can break the spell. The 'lemon' aspect might be some flirty and slightly spicy interactions as Harry tries to bring Hermione back to normal. For example, a scene where Harry has to hold Hermione's hand a bit longer than necessary while reciting a counter - spell.
Maybe the Goblet of Fire is cursed and it starts to affect the students' emotions. Harry and Hermione are not immune. The 'lemon' part could be their attempts to resist the strange lust - like feelings the curse is inducing. However, in their struggle, they end up getting closer. For instance, they find themselves in a situation where they have to stay close to each other to avoid the curse's full effect, and during this time, their relationship takes an unexpected turn towards a more romantic and passionate one.
A fanfiction might revolve around Hermione being entered into the Goblet of Fire by some dark magic. Harry is determined to protect her. The 'lemon' could be used to show the strong emotional and physical attraction between them as they face the challenges of the tournament together. For example, there could be a scene where Harry holds Hermione close after she narrowly escapes a dangerous task, and there's a moment of intense eye - contact and a hint of something more.
One possibility is that Hermione could use her intelligence to help Harry figure out the mysteries of the Triwizard Tournament earlier. For example, she might quickly decipher the clues related to the tasks. Maybe she could also prevent some of the dangerous situations Harry gets into. In the fanfiction, she could be more involved in Harry's training for the tasks, sharing her vast knowledge of magic to give him an edge.
The hug could signify deep friendship. In the 'Goblet of Fire' setting, they face so many dangerous situations. A hug is a way of showing they've got each other's backs. It's like a silent promise that they'll support one another through all the challenges.
A possible plot is that Harry gets angry at the unfair treatment he receives during the tasks of the Goblet of Fire. For example, in one task, he might notice that the other champions have some advantages that he doesn't. His anger then gives him the motivation to find a way to overcome these unfair situations and still succeed in the tournament. He could use his anger to fuel his creativity and come up with unique solutions to the challenges.
A possible plot could be that adult Harry is called back to Hogwarts due to some strange magical disturbances related to the Goblet of Fire. He realizes that there are remnants of dark magic from the tournament that were never fully eradicated. He then has to work with the current Hogwarts staff and students to find and neutralize these dark magic sources.
Well, their relationship could become more of a rivalry. Instead of being friends, they could compete with each other to solve the mysteries around the Goblet of Fire. Each trying to outwit the other in finding out who put Harry's name in the Goblet.
Well, a plot could involve Harry and Hermione being forced to enter the tournament together as a pair, against the rules. They then have to face challenges that are not only dangerous but also designed to test their relationship. For example, in one task, they might have to choose between saving each other or winning the task. This would create a lot of drama and tension between them. Also, there could be a sub - plot where they start to realize their feelings for each other during the tournament.
Another plot could involve Hermione using her vast knowledge to help Harry train for the tasks in the tournament in a more unique way. For example, she might find a way to combine ancient magic with modern spell - casting techniques. This could lead to some really exciting and unexpected moments during the tasks.
A possible plot could be that the Goblet of Fire starts acting strangely. McGonagall notices some odd magical fluctuations around it. She enlists the help of Hermione, knowing her academic prowess. Together they try to figure out what's wrong. Meanwhile, Harry has a strange feeling about it all. Eventually, they discover that a dark wizard from the past is trying to use the Goblet to return. And they must stop it before it's too late.
The fanfic might revolve around Harry's interaction with the Goblet of Fire due to a misunderstanding. He could think that the goblet is being influenced by dark magic and decides to investigate. As he messes with it, he discovers some hidden secrets about the Triwizard Tournament and its origins. This could lead to him having to make difficult choices to protect the integrity of the tournament and Hogwarts, all while dealing with the consequences of his meddling with such a powerful magical object.