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
In her human disguise, Lilith was a beautiful young woman, but in her true form, she was a hideous witch.
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.
1599
Through the words of William Shakespeare after the death of his son, she 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 their kind back into the universe using the Globe theatre along with the play Loves Labour’s Won, which was written by William Shakespeare. Lilith accomplished this first by influencing Shakespeare into having the play performed a specific night, and then by directly hypnotizing him and using a puppet to have him write the last few lines of the play as the spell needed to create a portal.
In 1599, the three Carrionites opened a portal to the Deep Darkness, 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 took. (TV: The Shakespeare Code)
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 Linley for threatening the production of Love Labour's Won, frightening Dolly Bayley to death and reminding the Doctor of Rose’s tragic fate. She also sadistically enjoyed driving Peter Streete outright insane rather than kill him, 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)