Wherever a player has progressed to in the raid, that player can lead a fireteam beginging at that checkpoint. Anyone, at any time, can join another fireteam leader at any point along the raid (Only thing I'm not sure about is if you can join someone at the last boss if you haven't gotten that far yet. I'm nearly positive that you can though).

Does anyone know how the lockout work for the Raid? If someone has progressed to the sixth boss with one fireteam, can they join another another fireteam from the beginning, or will they be locked out?

The fireteam leader is the one who stores the raid progress. You will continue from wherever your fireteam leader left off.