Once upon a time - однажды. "Жил-был" it isn't used in every day conversation. It is used just in tales as a start story. English tales start with "Once upon a time ...", Russian tales usually start with "Жил был Иван" = "Once upon a time lived man named Ivan"

Once upon a time

Жил-был (or жили-были) - I think it means "to exist/to live" In Russian this "жили-были" used at the very begining in fairy tales. Например: Жили-были старик со старухой.

Once there lived. "Жили-были старик со старухой и была у них курочка Ряба" - once there lived an old man with an old woman and they had a hen named "Ryaba" ("Курочка Ряба", a widely known folk tale)