Nelson Mandela's daughter just lost a $7.5 million battle in court -- because that's how much a judge ordered her to pay an L.A. boxing promoter ... after she allegedly flaked on a deal to organize a Pacquiao/Mayweather fight.

TMZ broke the story ... a guy named Duane Moody sued Nelson's daughter Zindziswa Mandela for $7.5 million earlier this year -- claiming she hired him to organize a Pacquiao/Mayweather bout for her father's birthday ... but ultimately flaked on the deal ... and the fight never materialized.