Lilith was a Carrionite who, like the rest of her race, was banished to the Deep Darkness by the Eternals.
Biography
Dawn of the universe
At the dawn of the universe, Lilith and the rest of her kind went to war with the Hervoken. The conflict proved so destructive that it forced the Eternals to step in and banish the Carrionites to another dimension known only as the Deep Darkness. (PROSE: Forever Autumn)
16th century
Through the words of William Shakespeare after the death of his son, Lilith and her mothers, Mother Doomfinger and Mother Bloodtide, were able to escape into the universe on Earth in 1598. From their arrival on into 1599, she helped influence in the construction of the Globe Theatre, persuading the architect, Peter Streete, to build the theatre so that it would have 14 sides.
This was part of a plan they had set in motion to summon the rest of the Carrionites back into the universe using the Globe theatre along with Shakespeare's play, Love's Labour’s Won. Lilith accomplished this first by influencing Shakespeare into having the play performed a specific night, and then by directly hypnotising him and using a puppet to have him write the last few lines of the play as the spell needed to create a portal.
When the play was performed, the portal was opened, allowing all other Carrionites to enter the universe, but they were stopped by Shakespeare after he created a phrase that closed the portal and trapped Bloodtide, Doomfinger, and Lilith in their crystal ball, which the Tenth Doctor then took (TV: The Shakespeare Code) and stored in the TARDIS' "C chest". (TV: The Unicorn and the Wasp)
Attempted Revenge
Lilith and her mothers escaped from their crystal ball after Harry Sullivan dropped it while he was bringing it to the Fourth Doctor. When they tried to kill him, the Doctor allowed the Reapers to enter the TARDIS and devour them. (PROSE: Toil and Trouble)
Personality
Lilith was very manipulative, often using her human guise to seduce men to lure them into a trap in order to kill them. She made it clear that she viewed men as nothing more than puppets to be used or toyed with. However, the Tenth Doctor was immune to such techniques.
She was also sadistic and took visible pleasure in controlling Shakespeare, ruthlessly killing Lynley for threatening the production of Love Labour's Won, frightening Dolly Bailey to death and reminding the Doctor of Rose Tyler’s tragic fate. She also sadistically enjoyed driving Peter Streete outright insane, resulting in him being committed to Bedlem Hospital. (TV: The Shakespeare Code)
References
When Rose-the-Cat asked the Tenth Doctor if Rose Tyler had ever said the "L-word" to him, he mistook her phrase to be a reference to Lilith's name; adding "she only broke one of my hearts and that was completely different!" (COMIC: A Rose by Any Other Name)