One interesting storyline could be the male OC being a powerful knight who is initially sent to spy on Cersei but ends up falling in love with her. He has to navigate the dangerous politics of King's Landing while keeping his feelings a secret. Another could be that the male OC is a foreign noble who comes to Westeros and forms an unexpected alliance with Cersei. They face many challenges together, like dealing with the other noble houses' plots against them.
A great storyline might be where the male OC is a maester in training. He catches Cersei's eye because of his intelligence and knowledge. Cersei uses him to gain an edge in the power struggles. But as time passes, the male OC realizes he's being used and tries to find a way to either change Cersei or break free from her grasp. This could lead to a complex and tense relationship filled with twists and turns.
Perhaps in fanfiction, Violet Lemon is a healer. Cersei, after being injured in a battle or political intrigue, is forced to seek help from Violet. This encounter changes Cersei's perspective as she sees kindness and selflessness in Violet that she's not used to. They then start a journey together, with Cersei learning from Violet about different values.
To develop the male OC, start with his goals. Maybe he wants to gain power and sees Cersei as a means to that end. His appearance can also play a role. If he has a striking look, it might attract Cersei's attention. His relationships with other characters are crucial too. If he has a close friend or mentor, they could influence his actions towards Cersei. For instance, if his mentor warns him about Cersei's dangerous nature, he has to decide whether to listen or pursue his own desires.
One plot idea could be an OC who is a healer and tries to cure Cersei of a mysterious illness that no one else can figure out. This could lead to a complex relationship between them as Cersei is not used to depending on others.
The male OC could be a sellsword who is hired to protect Cersei. At first, she looks down on him as a common mercenary, but he proves his worth by saving her life multiple times. This causes her to reevaluate her opinion of him and a relationship begins to develop. Another plot is that the male OC is a noble from a small house who has a unique claim to the throne. Cersei tries to use him for her own political gain, but in the process, they fall in love. And there could be a plot where the male OC is a minstrel, whose songs touch Cersei's heart and make her open up in ways she never has before.
You can start by looking on Archive of Our Own (AO3). It has a large collection of fanfictions, and there are likely many Cersei Lannister OC ones there. Just use the search function and type in relevant keywords.
In Cersei Lannister x OC fanfiction, the character dynamics can be very interesting. Cersei is a complex character with her own motives and desires. When paired with an Original Character (OC), it allows for new storylines. For example, the OC could be someone who challenges Cersei's power-hungry nature or perhaps becomes an unexpected ally. Their interactions might lead to power struggles, emotional turmoil, or even a strange sort of friendship. The key is how the author develops their relationship in the context of the 'Game of Thrones' universe.
Power is a common theme. Cersei is all about power, and when an OC is introduced, the power dynamic becomes a central focus. Whether the OC is trying to gain power through Cersei or is a threat to her power, it drives the story. Another theme is loyalty. Cersei values loyalty, but also has a hard time trusting. So, the OC's loyalty or lack thereof can create a lot of tension. Love can also be a theme, though it might be a twisted form of love, given Cersei's nature.
There's also 'Cersei and the Unknown Heir'. In this fanfiction, the OC is a supposed heir to a powerful house and how Cersei deals with this threat and possible alliance is the focus. It's full of political intrigue which is typical of Cersei's storylines.
To develop their relationship realistically, start with their initial meeting. If the male OC is from a different background, there should be some level of distrust or misunderstanding at first. For example, if he's from a poorer region and she's a Lannister, she may look down on him. As they interact more, small acts of kindness or shared interests can start to break down the barriers. For instance, if they both have a love for a certain type of horse, it can be a starting point. Their relationship should also be affected by the political climate around them. If Cersei's power is threatened, she may be more hesitant to show affection for the male OC for fear of looking weak.
She could also be on a quest for power. Inspired by her mother Cersei's thirst for power, she might start her own journey to gain influence. However, she may choose different methods than her mother. Instead of using manipulation and cruelty, she could focus on building alliances through kindness and mutual respect, which would be a huge contrast to the typical Lannister way.