Well, it could be that in this fanfiction, Lucius has some extreme expectations of Draco. Maybe Draco has made a mistake in the wizarding world's politics or in upholding the family's pure - blood image, and Lucius takes it upon himself to 'beat' Draco in a more than just physical sense, like crushing his spirit or self - esteem.
In this fanfiction, the scenario of Draco being beaten by Lucius could be set against the backdrop of the complex relationships within the Death Eater circles or the pure - blood society in the Harry Potter universe. It could explore themes like family loyalty, the harshness of the pure - blood upbringing, and the consequences of not meeting the family's and society's expectations.
I'm not sure specifically as there could be many different interpretations in different fanfictions with this title. It might involve a power struggle within the Malfoy family, perhaps Lucius punishing Draco for some perceived disobedience or failure.