Extra life mode is a separate game mode where it plays more like the original doom. Once all you lives run out, that's it game over. You can choose a difficulty so I would recommend play this on I'm too young to die. I would also recommend you play this on your second play through as if you collect everything during this play through, you will have to collect everything again if you are going for (master of fasting) achievement as you can not replay missions in extra life mode.
Note: you can beat the game with more then 10 extra lives. I finish that game with 47 and the achievement pop once the credits rolled.