At the start, Hermione would likely be angry. She's not one to take things lying down. Her anger could be a mix of being furious at Ron for breaking their relationship and also at herself for maybe not seeing the signs. This anger could fuel her decision to leave Ron and seek refuge or help from Lucius in the fanfic.
Hermione would probably be extremely hurt. She's a very loyal person, and to have Ron cheat on her would shatter her trust. She might become withdrawn, not wanting to talk to anyone at first, and just try to process the pain on her own. Then she decides to run to Lucius, perhaps because she feels she has nowhere else to turn, or she thinks Lucius can offer her some sort of solution or support.
She might be heartbroken. Hermione is a strong - willed character, but being cheated on would surely shatter her. She could initially be in disbelief, given her trust in Ron. Then, she might become angry and start to distance herself from Ron, focusing more on her own studies or other relationships, like her friendship with Sirius.
She might be extremely hurt and angry. In such a situation, running to Sirius could be her way of seeking comfort and support from someone she trusts. She could be feeling betrayed and might have a hard time believing that Ron would do such a thing.
Perhaps Lucius is bored with his current situation. Helping Hermione gives him something new and exciting to do. He might also want to show off his power and influence. By being the one Hermione runs to, he can prove that he is a force to be reckoned with, and that he can be the knight in shining armor, even if his intentions are not entirely pure.
Sirius could play multiple roles. Firstly, he could be a friend who listens to Hermione's rants and sorrows. Secondly, he might act as a protector, making sure Hermione doesn't do anything rash in her emotional state. And thirdly, he could be a catalyst for Hermione's growth. His presence could make Hermione realize that there are other aspects of life and relationships that she has been overlooking. His friendship could open up new opportunities for her, whether it's in terms of magical knowledge or personal development, all while she is dealing with the aftermath of Ron's cheating.
Ron would probably be shocked at first. He might stutter and not know what to say immediately. Then, a big grin would spread across his face as the news sinks in, and he'd pull Hermione into a tight embrace, telling her how happy he is.
Well, it could be that Lucius uses his powerful influence in the wizarding world. Maybe he intimidates Ron with threats related to his family's status or he uses some dark magic to create a distraction and whisk Hermione away.
Hermione might become more distrustful of Ron. After being saved by Lucius from Ron, she could start to see Ron in a different light, perhaps as someone with a darker side she hadn't fully recognized before. This could make her more cautious in her interactions with him.
He could also be heartbroken. Ron might withdraw into himself, spending a lot of time alone in his room at the Burrow, not wanting to talk to anyone. He may start to doubt his self - worth, thinking that he wasn't good enough for Hermione.
I'm sure there are. Fanfiction is a vast world where all kinds of scenarios are explored. A 'Ron cheats on Hermione' fanfic might be written to show the vulnerability of their relationship or to introduce new plotlines. But it's not something that would be acceptable in the context of the original story. It can be an interesting read for those who like to see different interpretations of the characters, but it also might be a bit controversial among die - hard fans of the original relationship.
Perhaps she tries to find them right away. Using her intelligence and resourcefulness, she starts to search for any clues as to where they might have gone. She could ask other friends, like Neville or Luna, if they have seen Harry and Ron. And she might be determined to bring them back, not willing to give up on their friendship easily.