Mr. Heartfilia was one of Fiore's richest men, running a major company that basically consumed his entire life. He was married to Layla, who's now deceased, and they had a daughter together—Lucy.
The thing is, he was a pretty absent father. He poured everything into his business and basically ignored Lucy growing up, which obviously messed with her head. She felt rejected and built up real resentment toward him over the years. Eventually it got bad enough that she just ran away from home rather than stick around.
Content compiled by AnimeList.moe from publicly available sources.
