[7] While studying English at the University of Sheffield,[8] Prebble wrote a short play called Liquid, which won the PMA Most Promising Playwright Award.

The production's Broadway transfer opened at the Broadhurst Theatre in April 2010 but failed to match the critical acclaim it received in the UK and closed the following month.

[13][14] The Associated Press wrote of the production, "Playwright Prebble and director Rupert Goold attempt to walk a fine line in the production, which is alternately naturalistic and highly stylized in its depiction of the rise and fall of the mammoth energy company that engaged in accounting fraud on an unprecedented level.

"[15] The Effect, a study of love and neuroscience, premiered at the National Theatre in 2012, won the 2012 Critics' Circle Award for Best Play.

[16] The Effect premiered in the US Off-Broadway at the Barrow Street Theatre on 2 March 2016, directed by David Cromer, and featuring Kati Brazda, Susannah Flood, Carter Hudson and Steve Key.

[18] In April 2017 it was announced that Prebble was working on a new play, based on Bizet's Carmen[19], from the new Bridge Theatre in London.

[20] In October 2018, London's Old Vic announced Prebble's A Very Expensive Poison, a stage adaptation of Luke Harding's non-fiction book of the same name.

Set in modern day London, the show revolves around a young woman, Hannah Baxter, played by Billie Piper who lives a secret life as a call girl.

The series received positive reviews with Nancy Franklin of The New Yorker comparing the series favorably to Sex and the City writing, "The show also uses London in somewhat the same way “Sex and the City” used New York—we see a lot of bright lights, fancy restaurants, and expensive apartments—though there is a sadder, more wistful quality to the photography here".

[29] From 2018 to 2023, Lucy served as a co-executive producer and writer on the acclaimed HBO drama Succession starring Brian Cox, Jeremy Strong, Sarah Snook, Kieran Culkin, and Matthew Macfadyen.

Scott Tobias of Vulture praised the episode writing, "it’s such a great opportunity to get to know the significant others in the Roys’ lives and see how they interact with their mates — and, hilariously, with each other".

Lucy Mangan of The Guardian praised the collaboration between Prebble and Piper, calling the show a "wild ride that feels like an absolute gift.