After the events of The Terror of Trigon, Lilith stayed on with the Titans briefly, during which time she accompanied the team on a trip to Wonder Girl's home island of Themyscira.
During this mission into the realms of Greek myth, Lilith finally
learned her true parentage: her father was a normal human who had been
seduced by Thia,
the mythological Greek Titaness of the sun. The power-hungry Thia
attempted to take over Olympus, but the young mortal Teen Titans helped
defeat the Titans of Mith and returned home safely—all except Lilith, who elected to remain on Olympus, claiming her birthright as a demi-goddess. (extracted from Wickipedia)
This was the shorter origin ever, because after Crisis on Infinite Earth her story has been changed.
Anyway, as goddess, Lilth wore a fantastic costume, created by the great José Luis García Lopez.