Barbamon is the father of Lilithmon & SkullSatamon.
Barbamon arrives on the moon in search of the legendary Zeo Crystal. He very nearly succeeds, capturing both the Crystal & the DigiDestined's Digimon, & even throwing an "End of the World Party" in the Youth Center, before entering battle against the DigiDestined themselves. Barbamon grows to giant size & survives the finishing attacks of both NinjaOmnimon & ShogunOmnimon. On his retreat to the moon, he considers the failure nothing but a minor setback & decides to stay.
Barbamon later sends his old ally Sanzomon to battle the DigiDestined, & she nearly succeeds in taking control of the DigiDestined's minds. Barbamon is foiled once again, however, as Sanzomon meets her end courtesy of ShogunOmnimon.
Barbamon then summons the Orb of Doom to the Earth, which he uses to revert the DigiDestined to powerless children. He prevents Tactimon, Lilithmon, MadLeomon, & SkullSatamon from destroying Tokyo, revealing that he has more plans for the Earth. He sends a selection of Digimon to invade the planet, led by his field general, Tengumon. When the invasion is defeated by the Aqua Warriors, Barbamon throws a tantrum & flees back to his home dimension, where he says evil always wins.
When the Machine Empire arrives on the moon, Lilithmon calls Barbamon & begs him to let them stay with him. Barbamon agrees, despite the fact that Lilithmon will be bringing "that husband of hers."