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.
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 She might become withdrawn, not wanting to talk to anyone at first, and just try to process the pain on her own.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.
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.
There might be some out there, but this is a rather non - canon and often controversial concept in the Harry Potter fanfiction world. Some people might write it to explore different relationship dynamics or create drama, but it goes against the normal pairings and character traits we know from the original series.
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.
One possible plot could be that in a dark and alternate version of the wizarding world, Ron has been influenced by some dark magic or a powerful enemy who has turned him against Hermione. Lucius, for his own reasons (maybe to redeem himself or because he sees the value in Hermione), steps in to save her. He might use his powerful family connections and knowledge of dark magic to counter whatever threat Ron poses.
Another plot twist could be that Lucius's act of saving Hermione causes a rift between Hermione and Ron that is hard to repair. Ron might misunderstand Hermione's connection with Lucius and think she is now on the 'dark side' so to speak. This could lead to a complex love triangle situation where Hermione has to prove her loyalty to her friends while also dealing with her gratitude towards Lucius.
One consequence could be that it creates a rift between Ron and Hermione. Hermione might be grateful to Lucius, which could make Ron jealous or angry. This could lead to a strain in their relationship, and they might have to work through their feelings about Lucius' interference.
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.
Maybe Lucius wants to gain an advantage. He could see Hermione as a powerful witch with knowledge that he can use for his own ends. By saving her from Ron's beaten, he hopes to earn her gratitude and get access to her skills or information.
One reason could be to create drama. By having such a scandalous situation in the story, it can generate a lot of emotional turmoil among the characters and keep readers on the edge of their seats.