It's one of the urban myths of the show, kind of like never seeing Wilson's face in "Home Improvement", or Arnold's last name in "Hey Arnold". In the beginning of the show, Lane used to mention "My parents" when referring to her guardians, not "My Mom" or "My Parent" singular. We assumed there was an intent for a Mr. Kim, but as time passed and the Palladino's never filled the role for him, there really wasn't a suitable explanation for his presence/absence, so they never wrote him in, and Lane started just talking about her mom.

In the context of the story, however, we have to assume Mrs. Kim was married since she said so and Lane wasn't a bastard child because that goes against everything Mrs. Kim has ever said. Basically, he exists in theory, lol! I hope that explains it somewhat.