Bribery, Trade, or Begging

Harry could offer to pay Lucius Malfoy something in restitution. It couldn't just be money or an incredible favor. As the original 'Taboo Tradeoffs' paper mentions, people only get more angry when you try to do that. Harry would need an accurate model of Lucius suspecting him as Harrymort and be able to trade him something that Harrymort would consider sacred.

• Trade his invisibility cloak to Lucius for Hermione's freedom. Make sure to play up that it is 1/3rd of the Deathly Hallows and thus something Harrymort considers sacred/invaluable.

• Trade Lucius a blood debt from the House of Potter.

• Make an unbreakable vow to protect Draco or otherwise help Lucius (or some other ritual).

• (Assuming Roger Bacon's diary is indeed the diary Horcrux and Harry manages to discover that) Trade Lucius a piece of Voldemort's soul as apology.

None of the trades seem particularly smart or likely, but Harry might consider a few of them if he got really desperate. They seem to be of sufficient value to Lucius (or rather, to Harry's model of Lucius' model of Harrymort) to prove that Harry is genuinely sorry and be worth Hermione's life/magic/future.