The order (specified in the spoiler) is important.

Some specifics are still unclear/being researched, but this are the best guesses at the moment: As said before, apparently it has to be done in a specific order to work and anything getting in the way resets the process. Replicating the deaths is easier said than done. The task of the player, at this point, is to recreate these deaths with the appropriate characters. These 4 puzzles, when completed, show the game over screen for the 4 characters and their cause of death. You can assign each piece to a different puzzle thanks to the little markers beside it: There are 4 different puzzles and each one of them belongs to a different character. This item apparently does nothing in terms of gameplay, but when dying in a Sacrifice Room (the empty ones with a single set of spikes at the center) while carrying it, you'll get a game over screen with a puzzle piece replacing the cause of death. The first step to the discovery starts with the Missing Poster trinket. The sequence of steps to unlock the Lost is not explained anywhere in the game and requires a long process to be discovered. There's anyway a longer explanation tied to the character. dying in another location, or with another character) will reset the sequence, so you'll have to start again with Isaac. The deaths have to happen in this order and any mistake (i.e. The fight after the Fallen is guaranteed to work, it's still unclear if the second stomping phase works too. Azazel must be killed by Satan in Sheol. Judas has to die stomped by Mom's foot in the Depths/Necropolis

Maggie must blow herself up with a bomb in the Caves/Catacomb Isaac has to be blown up by a Mulliboom in the Basement/Cellar You have to perform a sequence of specific deaths with 4 different characters at specific locations: The short version, with just the instructions to unlock the character, is under the spoiler: The Lost is meant to be the most secret and elusive unlockable character in the new Binding of Isaac.

The lost binding of isaac