Die to Mom during the Mom boss fight as Judas (Use the seed PC8EVHFD to ensure you get the Technology 2 laser, as well as IPECAC, which increases the laser damage - making it easier to get to Mom.).Kill yourself with bombs as Maggy in the Caves/Catacombs (Use the seed 2VPHDMBS to get the Dr Fetus item, ensuring that you have bombs to kill yourself with when you reach the floors).Die to a Mulliboom as Isaac in the Basement/Cellar (Use the seed JTMDEZPF to ensure a Mulliboom in the room below).You will get a puzzle piece revealing the next death that you must take in order to unlock this character.
The Lost is unlocked in a very specific way by dying in a particular order, which can first be found out by dying in a Sacrifice Room with the Missing Poser or Mysterious Paper trinket.