It seems almost impossible to achieve wins with the Lost to unlock the respective items (-0- Baby, Isaac's Heart, The Body, The Soul, The Mind, D100, Godhead).
How does one win as this character?
There are various items increasing your chances as The Lost, namely 9 Lives, 1up, Holy Mantle and severe damage-ups.
However, there is actually a way guaranteeing victory on any run - it involves using pseudo-savestates and thus may be considered "cheating" by some people.
Nonetheless, this is how it works:
You can abuse the ability to continue a run to your advantage - if you "soft-exit" the game via the ingame menu and the option "Exit to Menu", you create sort of a checkpoint, the game remembers this last room. Such checkpoints are automatically generated at the start of every floor.
Now, when you get hit as the Lost and escape to the menu before the death screen pops up, you will still be unable to continue the run. However, if you "hard-exit" the game (as in: close the game window) during that, you can resume from your last set checkpoint as if nothing had happened. This assures, assuming you are quick enough on the draw to pause the game and hard-exit before the death screen, that you will be unable to lose the run. It is important to note that this only works when you get hit - if you hard-exit normally, you will resume from the room you were last in (something that will be problematic if you tried to do it in a curse room, for example).
So the strategy to minimise agony is to create a checkpoint via soft-exiting the game after tough rooms to ensure a steady progress. This even allows to check for the contents of curse rooms by creating a checkpoint, entering the curse room and then hard-exiting your game once you take the hit from exiting the room.
Ideally you'd want a strong run to abuse this strategy, just to minimise the amount of times you have to hard-exit the game and return.