Well, perhaps Snape has some desperate reason. Maybe he's trying to protect Lily from the Dark Lord in his own twisted way. He might think that by taking her away from the wizarding world for a while, he can keep her safe from Voldemort's reach.
One possible plot is that Snape has discovered a prophecy that involves Lily and he believes that the only way to change the outcome is to keep her in isolation. So he kidnaps her, but Lily, being the strong - willed character she is, tries to fight back and change Snape's mind throughout the ordeal.
In this fanfiction, it could be that Snape kidnaps Lily out of jealousy. He sees her getting closer to James Potter and in a fit of rage and possessiveness, he decides to take her away. He might plan to convince her that he's the better choice while she's held captive.
It could end with Lily escaping and being forever angry with Snape. She might cut all ties with him and go on to marry James Potter, with Snape left full of regret for his actions.
One possible plot twist could be that Lily marries Snape out of a sense of duty. Maybe she discovers some long - hidden secret about Snape's past that makes her feel obligated to stand by him. For example, if she finds out that he made a great sacrifice for her family in the past that no one else knew about. Another plot twist could be that it's a marriage of convenience. The wizarding world is in danger, and their union is seen as a way to bring two powerful magical lineages together to fight against a common enemy. Or perhaps Snape has some unique magical ability that Lily needs in order to achieve a certain goal, and marriage is the only way to access it.
It could also be due to some external factors. Maybe there are threats from dark forces that he doesn't want to involve Lily in. If he is getting deeper into the dark arts or some dangerous situations, he might choose to give up on her to protect her from the potential harm that could come her way because of his associations.
In this fanfiction scenario, Snape might be under the influence of a dark spell or some form of blackmail. He kidnaps Harry as a result. However, Harry, being the resourceful character he is, might start to figure out Snape's true situation and try to help him break free from whatever is controlling him.
One common plot twist is when Lily discovers Snape's deeper involvement with the Dark Arts later than expected. This realization makes her lash out at him more harshly than before, causing great pain. For instance, she might find out about some of his secret experiments or associations.
In this fanfiction, perhaps Snape finally gets the chance to truly apologize to Lily. He might express all the unspoken feelings and regrets he had when she was alive.
One possible plot could be that Erik, being the complex and often misunderstood character, kidnaps Christine out of his obsessive love for her. He might take her to his lair, thinking he can protect her from the outside world which he believes is full of people who don't truly appreciate her talent. Then Christine could struggle between her fear of Erik and her understanding of his tortured soul.
One possible plot could be that Tsunade kidnaps Naruto because she believes an enemy is after him and she wants to keep him safe in a secret location. She might think that by taking him away from the village, she can train him without any distractions or threats.
One possible plot could be that Toothless is under some sort of spell or mind control. Maybe a new villain in the How to Train Your Dragon universe has the power to manipulate dragons. Toothless, being a powerful Night Fury, is forced to kidnap Hiccup. Hiccup, of course, tries to figure out why Toothless is acting this way and how to break the spell.
Well, in such a fanfiction, Itachi might kidnap Hinata for various reasons. Maybe he's being controlled by some dark force and needs Hinata for some ritual. Or perhaps he's been misinformed that Hinata has some special power that can help him in his secret mission against the Hidden Leaf Village.