Common themes in this type of fanfiction often revolve around change. The oc replacing Lucy is a big change in the story's dynamic. This can lead to themes like acceptance - both the oc having to accept their new situation and the other characters in the story having to accept the oc in Lucy's place. Another theme could be exploration. The oc might explore aspects of the story world that Lucy either didn't get to or did in a different way. It could also be about challenging the status quo. Since the oc is a new element, they might disrupt the normal flow of the story and bring about new ideas or ways of doing things, which is an interesting theme to explore in this kind of fanfiction.
I'm not sure specifically which 'oc replaced lucy fanfiction' works are out there. You could try searching on popular fanfiction websites like Archive of Our Own or Fanfiction.net. Maybe start by using the exact phrase in their search bars.
The plot could involve jealousy. Lucy might become jealous of Lisanna as she takes over her position in the guild. This could drive Lucy to train harder and become more independent. Maybe she'll find a new group of friends or allies who see her value outside of the guild.
In a fanfiction of Lucy being replaced by Lisanna, it might explore the emotional turmoil of Lucy. She could be heartbroken seeing how easily she was seemingly replaced. Meanwhile, Lisanna might not be fully aware of the situation or might be caught up in the sudden popularity. This could create a rift not only between Lucy and Lisanna but also within the guild as a whole. Some members might side with Lucy, feeling that she was unjustly pushed aside, while others might be excited about Lisanna's presence and not understand Lucy's pain.
To develop their relationship, start with small interactions. Have the OC offer to help Lucy with her celestial spirit summoning, like finding a rare ingredient for a spirit - summoning spell. Then, they could have some shared experiences, such as getting trapped in a cave during a mission. This forces them to rely on each other, talk, and get to know one another better. Another way is to give them common goals. For example, they both want to defeat a certain dark mage who has been causing trouble in the area. Working towards this goal together will bring them closer.
One possible plotline could be that the oc has a different set of skills or powers compared to Lucy, which changes the way the story unfolds. For example, if the oc is a magic user with a more aggressive style in a world where Lucy was more of a support - type magic user.
A common theme is friendship. The oc and Lucy often start as friends and then the relationship may develop further. Another theme is adventure. They usually embark on some exciting adventures together in the fictional world.
I'm not sure specifically about 'oc replace lucy' fanfiction. You could try searching on popular fanfiction websites like Archive of Our Own (AO3) or FanFiction.net. Just type in relevant keywords in their search bars, and you might find some stories that fit this concept.
It could be that the fan OC has a very strong connection to Lucy on an emotional level. They constantly dream about being like her. One day, they enter a virtual reality world that is based on Lucy's world. In this world, their avatar starts to take on Lucy's form because of their subconscious desires. As they spend more time in this virtual world, the transformation becomes more and more permanent, and when they finally exit the virtual world, they find that they have become Lucy in the real world as well, through some kind of magic that blurs the lines between the virtual and the real.
Another theme is the exploration of magic. Lucy has her celestial magic, and the OC usually has some form of unique magic as well. The fanfictions often explore how their different magics can work together or clash. It's interesting to see how the authors play with the magic system in the Fairy Tail universe to create new and exciting storylines for Lucy and the OC.