RORY: When are you going to let your parents know that you listen to the evil rock music? You’re an American teenager, for God’s sake.
Lane has two parents, but her father is never seen during the course of the original show, even at major family events. It is never explained where he is, and Keiko Agena, who played Lane, never asked Amy Sherman-Palladino where Mr. Kim was. Keiko herself felt that he had to travel a lot, and that it might have something to do his religion, such as missionary work of some kind. Perhaps he was always out buying new stock for the antique store. A Year in the Life provides a brief glimpse of Mr. Kim, confirming once and for all that he does exist.
The Annotated Gilmore Girls 