Yes, there might be some. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for the key phrase 'Lucius gives Draco riding lessons' in the search bar and you may find some interesting works.
In this fanfiction concept, it could be really interesting. Maybe Lucius is teaching Draco how to ride a broomstick. Lucius might be a strict but effective teacher, passing on his own skills and knowledge. Draco could initially struggle but gradually improve under his father's guidance.
One plot idea could be that through the riding lessons, Draco discovers a new side of his father Lucius. Maybe Lucius is softer and more patient during the lessons than Draco expected.
Well, Draco might be a bit nervous at first. Lucius could start by showing him the basics, like how to hold the reins or the broomstick properly. Then they could move on to more advanced things.
In a fanfiction about Draco and Lucius' broom - riding lessons, the setting might play a crucial role. Are they having these lessons at Hogwarts? Or perhaps on the Malfoy estate? If it's at Hogwarts, there could be interactions with other students or teachers. For example, they might face some rivalry from Gryffindor students who are also good at broom - riding.
You might also see some magical elements specific to broom - riding. For instance, the type of brooms they use could be important. Are they using the latest and most expensive brooms? And how do they customize them? The lessons could involve not just the physical act of riding but also the magic involved in making the broom perform better. There could be spells that Lucius teaches Draco to enhance the broom's speed or stability.
Draco's relationship with Lucius could develop in a more positive way. As Lucius teaches Draco flying, Draco might start to see his father in a new light. He could gain a new respect for Lucius's skills and knowledge. For example, if Lucius shows Draco some advanced flying techniques, Draco might be in awe of his father's abilities and feel closer to him.
Lucius might change too. He could start to see Draco more as an equal rather than just his son to be molded. Through the broom lessons, he realizes that Draco has his own ideas and ways of doing things when it comes to flying, and this makes him respect Draco more.
One common theme is power. Given Lucius's high status in the wizarding world, power dynamics play a big role. There's often a struggle for control or a shift in power within their relationship. Another theme is family secrets. The Malfoy family has a lot of secrets, and in these fanfictions, these secrets are often related to the nature of Draco and Lucius's relationship. For example, it could be about a hidden prophecy or a past event that binds them in a certain way.
Another theme is redemption. Sometimes, Draco or Lucius might be portrayed as seeking redemption in the eyes of the other. This could be related to their actions in the original Harry Potter series, and the fanfiction explores how their relationship can be a part of that journey towards redemption.