Lilith is Natalie's mother as well as the mother of all other "Lilim" demons, and a powerful demon of Hell in her own right.
Personality
Although beautiful and seemingly kind, Lilith is a hateful and sadistic creature of Hell, eager to corrupt and destroy those who attract her attention. Eric(a)'s interactions with Natalie have unfortunately made them a very interesting person to Lilith.
Background
Lilith was supposedly the first human woman when God created the world and the greater multiverse. However, she rejected both her husband-to-be "Adam the Fool" and also God, which was the act that made God drive her out of paradise in his fury. After these events, she wandered the worlds until she was noticed by a powerful demon, or indeed several, and after copulating with them birthed the very first Lilim, with more being born ever since until Natalie herself (who is the 666th Lilim).
...But if this origin story is actually true or made up because Lilith felt like it is anyone's guess.
Interactions
During Natalie's affection route, Eric(a) will eventually mail Lilith a letter asking for the name of Natalie's father. In response, Lilith teleports Eric(a) to Hell in order to learn how her daughter is doing before torturing them for all eternity. It is only after Natalie arrives and intervenes with Mr. Huggy Bear, her angelic stuffed toy, that Lilith relents and lets Eric(a) go.