Getting from Lab One to Lab Three required a mutant's eyeball, and getting from Lab Two and to Lab Three isn't that easy either. The goal is to get two items, a console keycard from a huge, adolescent deathclaw in the south room (the hard part) and a wedding ring, that contains the code used in combination with the keycard. The ring lies on a console near a dead vault dweller, in a computer room east in Lab Two, just past a few rooms with deathclaws.
The ring's inscription reads "9-29-2001", obviously a wedding date. Use the first three digits when inserting the card into the console and the door opens.