Lilith is a demon. As you know, if people die in the games, they get revived afterward. But anyone who suicides gets taken to Lilith instead.

We don't know very much about her so far... What we do know is that she will give you a choice to either stay in whatever corner of Hell she lives in to be tortured for eternity, or come back here after paying a price. It seems like the price is different for everyone, but it usually involves some kind of permanent, unhealable modification to your body.