There's a surprising amount of variety under that umbrella, honestly. The most common one, and my personal guilty pleasure, is the 'Soulmate Mark' or 'Soul Bond' trope. Everything starts with some magical, undeniable proof that they're linked—a name appearing on skin, a shared dreamscape, an uncontrollable empathic connection. It forces them into proximity, and the fun is watching proud, prejudiced Lucius and stubborn, righteous Harry grapple with a bond they both initially despise. The antagonism-to-reluctant-care is the core of the appeal; the magic just removes the option of walking away, which lets writers dig into forced proximity and political maneuvering in a way a simple school rivalry can't.
Another huge category is the 'Time-Travel' or 'Dimension Travel' fix-it. Usually Harry goes back, often as an adult, and ends up interacting with a younger Lucius—sometimes at Hogwarts, sometimes in the post-Voldemort political scene. The power dynamics flip; Harry holds all the future knowledge and often a weary, hardened competence that a young, ambitious pureblood like Lucius finds fascinating. It's less about romance initially and more about strategic alliances and changing history, with the relationship developing from a partnership of mutual advantage. You see a lot of aristocratic world-building in these, with Harry learning pureblood customs and Lucius reevaluating his prejudices.
Then you have the 'Draco's Friend Harry' or 'Hogwarts Era' variants, where the relationship starts earlier, often because Draco and Harry become reluctant friends or allies. Lucius gets involved as a parental figure, initially as a threat or a manipulator, but through observing Harry's character (and his influence on Draco), his view softens. These can skew towards hurt/comfort, with Lucius offering protection Harry never had from the Dursleys or Dumbledore. The tension comes from the inherent imbalance—it's a minefield of ethical issues, which is why the best fics in this vein spend ages building trust and challenging power structures.
Finally, the 'Post-War Political Marriage' trope is a staple. To secure peace or rebuild the wizarding world, a truce is brokered via a marriage contract between Harry, the symbol of the Light, and Lucius, a pardoned but still influential figure of the old regime. It's pure political drama and slow-burn negotiation, two people learning to coexist and then cooperate, often discovering that their public personas mask private compatibilities. The appeal is in the intellectual dance, the unspoken agreements, and the gradual erosion of formal hostility into genuine respect, and sometimes more.