Lenkiewicz was born in Plymouth, Devon, the daughter of James Pascoe. She attended Hyde Park Junior School and then Plymouth High School for Girls before progressing to a BA in Film and English at the University of Kent from 1985 to 1989, then later to a BA Acting Course at the Central School of Speech and Drama from 1996 to 1999. Initially she worked as an actor at the Royal Shakespeare Company and the Royal National Theatre, notably in Sir Peter Hall's production of The Bacchae. Her sister is the artist Alice Lenkiewicz her brother is the artist Wolfe von Lenkiewicz, who are both the children of the artist Robert Lenkiewicz. Their other brothers are Peter Mills and Thomas Mills.
Lenkiewicz's first play was Soho: A Tale of Table Dancers which she wrote for the Royal Shakespeare Company Fringe in 2000. It won a Fringe First award at the Edinburgh Festival Fringe. Helen Raynor's production was revived in London on 2 February 2001, the first play to be staged at the Arcola Theatre. Lenkiewicz also appeared in the play in the role of Stella.
Her second play, The Night Season (2004), set in Sligo, tells the story of an Irish family, the Kennedys, and their attempts to find love. It was staged at the Royal National Theatre in the Cottesloe auditorium by Lucy Bailey.
In July 2005 Lenkiewicz's Shoreditch Madonna, directed by Sean Mathias, was performed at the Soho Theatre. A tale of love among the artists in an East London gallery, it starred Francesca Annis and Leigh Lawson.
In 2006 Lenkiewicz wrote the script for the dance drama, Justitia, which was directed and choreographed by Jasmin Vardimon. It was initially performed at the Peacock Theatre and has since been on tour.
From February to May 2006, Lenkewicz's play Invisible Mountains toured London schools as part of the National Theatre "Interact" project.
In January 2006 she and Abdulkareem Kasid created a new version of The Soldier's Tale, a music theatre piece by Igor Stravinsky and Charles Ferdinand Ramuz, set in Iraq. It was staged at the Old Vic.
In August 2006, her hour-long play Blue Moon Over Poplar was staged by the National Youth Theatre company at the Soho Theatre as part of the NYT's Golden Jubilee.
In April 2008 her new adaptation of Ibsen's An Enemy of the People opened at the Arcola Theatre, directed by its founder Mehmet Ergen.
Her play Her Naked Skin, directed by Howard Davies, premiered on the Olivier stage at the NT in July 2008. It describes the struggles faced by two suffragettes immediately prior to World War One.
Also in July 2008, Lenkiewicz's Faeries, was staged at The Egg, Theatre Royal Bath. Faeries is an original drama for children, using puppetry. It tells the story of a girl evacuated during World War II, and the adventures she has when she spends a night in the park. It was commissioned by the Royal Opera House.
Her play, The Lioness (June 2010) was performed at the Tricycle Theatre. It describes meetings that Elizabeth I had with John Knox and the Earl of Essex.
Lenkiewicz adapted Ibsen's Ghosts for a production at the Arcola Theatre in August 2010.
The National Youth Theatre, at the Tramway Theatre in Glasgow, performed Stars over Kabul (September 2010). It tells the story of a young woman growing up in Kabul.
In January 2011 her play The Painter on the life of J.M.W. Turner premiered at the Arcola Theatre to mark its move into new premises.
Lenkiewicz's adaptation of Henry James' novella The Turn of the Screw was performed at London's Almeida Theatre (18 January – 16 March 2013). It was directed by Lindsay Posner
Lenkiewicz's shorter works include a contribution to 24 Hour Plays (June 2005), Flowers in her Hair (March 2009), the radio play, The Man in the Suit (April 2010), The Typist (June 2010), That Almost Unnameable Lust (Nov 2010). She translated Avec Norm (2004) by Serge Boucher, which was performed in a public reading at the Centre des Auteurs Dramatiques (31 July 2007).
In 2014 Lenkiewicz wrote a short play,We Two Alone, inspired by King Lear and commissioned by RIFT Theatre for their Shakespeare in Shoreditch Festival. The production was directed by Tess Farley and Connor Abbott of Outbreak Theatre.
Her play, The Invisible was directed by Michael Oakley at the Bush Theatre. It ran from 3 July - 15 August 2015.
Lenkiewicz has written playscripts for BBC Radio: Fighting for Words (2005), Caravan of Desire (2006), Blue Moon over Poplar (2006), The Man in the Suit (April 2010), Sarah and Ken (2010), Betty Lives in a Little Yellow House in Texas (2010), Burning Up (2011), The Phone (9. April 2011), an adaptation of Dracula (2012), The Winter House (2012), and a dramatisation of Anne Tyler's Dinner at the Homesick Restaurant (May 2013) and Ladder of Years.
Lenkiewicz co-wrote the Polish-language film Ida (2013) with Paweł Pawlikowski, its director. The film is set in Poland in the 1960s and is the story of what happens when a novitiate nun first learns that she is an orphan of Jewish parenthood. The first version of the screenplay was written in English by Lenkiewicz and Pawlikowski, when it had the working title Sister of Mercy. Pawlikowski then translated the screenplay into Polish and revised it. The screenplay for Ida won the European Screenwriter category at the 27th European Film Awards in 2014, and the Oscar for Best Foreign Film at the ceremony on 22 February 2015.
Several of Lenkiewicz's plays have been published individually, and in 2013 Faber & Faber published a collection.
Lenkiewicz was awarded the Critics' Circle Theatre Award for the most Promising Playwright 2004.
Lenkiewicz was awarded an honorary degree by the University of Kent at Canterbury on 12 July 2012.
Lenkiewicz co-wrote the screenplay for Ida which won the Oscar for Best Foreign Language Film, the European Film Award and the Bafta in 2015.