A "living dex" is a fan designation for when a player completes the Pokédex and has one of each species in the PC or the party at the same time. It's often considered to be much more difficult and time-consuming than a regular Pokédex because it often involves, for instance, playing the same game multiple times to get multiple copies of a Legendary Pokémon.
The method by which you can get a (mostly) completed Pokédex on Crystal is described here. This page will focus more on requirements specific to a living dex (without access to Red, Green, Blue, or Yellow).
You will need access to at minimum three separate save files of Gold, Silver, or Crystal in order to obtain all starters. Since you can breed them, only three files are required.
This is just to note that if you have access to a GS Ball Celebi, keep in mind that Gold and Silver cannot obtain it. if you wanted to, for instance, complete a living dex of Gold or Silver and Crystal simultaneously, you would need to get multiple Celebi in Crystal, requiring multiple save files that will each need to defeat the Elite Four.