You can start by looking on popular fanfiction websites like Archive of Our Own or FanFiction.net. Use the search terms 'Harry Potter', 'Snake', and 'Lemon' and see what comes up. Just be aware that the 'lemon' part might be a bit of an odd or specific element, so you may need to sift through some results.
There might be fanfictions where the snake in 'Harry Potter' has some sort of encounter with a lemon - themed magic. For example, perhaps the snake is lured by the scent of a lemon - scented magical potion and that leads to an interesting chain of events. But these are just speculations as there are so many creative interpretations in fanfiction.
If we consider a non - adult take on 'lemon' in fanfiction, it could be about a bright, citrus - like charm or potion that has some significance in the story. For instance, a lemon - scented potion that is used to enhance concentration during exams at Hogwarts. This kind of fanfiction can be light - hearted and family - friendly.
It could be Nagini. Even though in the original series she was more of a servant to Voldemort, in the fanfiction, she could have a different personality and form a bond with Harry.
It could also be a snake from the Forbidden Forest. There are many unknown and mysterious creatures in there. A snake from that forest might be more in tune with the natural magic of Hogwarts. Harry, being the curious and kind - hearted person he is, might come across it during one of his adventures in the forest and start a friendship with it.
The snake's help could represent an unexpected alliance. In the Harry Potter series, snakes are often seen as symbols of Slytherin, which is usually at odds with Harry. So it's significant as it breaks the stereotype of enmity between Gryffindor (represented by Harry) and Slytherin.
The snake might use its ability to move stealthily. It could spy on the enemies for Harry Potter. For example, it can slither into hidden places where humans can't easily reach and gather important information.
Maybe it's an anonymous gift from someone who has been observing Harry. This person could be a former student of Hogwarts who has a special connection to snakes and sees that Harry has a kind heart and would take good care of the snake. So they leave the snake for Harry to find with a simple note that just says 'For Harry Potter'.
Snake magic in Harry Potter fanfiction can be used to show a character's dark side. Since snakes are often associated with Slytherin and dark magic in the original series, in fanfiction, a character using snake magic might be on a path towards the dark arts. For example, they could use snake magic to control others or gain power in a more underhanded way.
One concept might be that the lemon has a prophecy written on it in snake language. Harry, being the only one who can understand snakes, has to decipher it. This would tie in his Parseltongue ability in a new and exciting way within the fanfiction.
Perhaps he would name it 'Slyther', as a play on the Slytherin house name. Given that snakes are often associated with the Slytherin house in the Harry Potter universe, it would be a fitting name for his pet snake.