Lloyd is from Bristol. After graduating from Birmingham University in 1979, she spent five years working in BBC Television Drama. In 1985 she was awarded an Arts Council of Great Britain bursary to be Trainee Director at the Wolsey Theatre, Ipswich. The following year she was appointed Associate Director at the Everyman Theatre, Cheltenham, then in 1989 Associate Director of the Bristol Old Vic, where her production of The Comedy of Errors provided her with a calling-card . She moved on to the Royal Exchange Theatre, Manchester where she directed The Winter's Tale, The School for Scandal, Medea, and an acclaimed production of Death and the King's Horseman by Wole Soyinka . In 1991 she made her debut at the Royal Shakespeare Company with a well-received production of a little-known play by Thomas Shadwell, The Virtuoso. Although she followed this in 1992 with a successful production of the rarely-seen Artists and Admirers by Alexandr Ostrovsky, she has, as of 2007, never returned to the RSC.
Also in 1992 came her first commercial success: her Royal Court Theatre production of John Guare's Six Degrees of Separation transferred to the West End. In 1994 she made her debut at Royal National Theatre with a production of Pericles which divided the critics . There was general praise, however, for her productions of Hysteria by Terry Johnson at the Royal Court and Bertolt Brecht/Kurt Weill's The Threepenny Opera at the Donmar Warehouse.
By this time, Lloyd's work had come to the attention of Nicholas Paine, then running Opera North. For her debut as an opera director he steered her to what was, at least in the UK, an obscurity - L'Etoile by Chabrier. The production was a great success, setting Lloyd on a significant and award-winning career as an opera director. Productions since then include La Boheme, Gloriana, Cherubini's Medea, Albert Herring and Peter Grimes for Opera North; Dialogues of the Carmelites for English National Opera/Welsh National Opera; Verdi's Macbeth (for the Bastille Opera and the Royal Opera House Covent Garden); the premiere of Poul Ruders' opera The Handmaid's Tale (from the novel by Margaret Atwood); and a controversial Ring cycle for ENO. She also directed a film version of Gloriana for which she received an International Emmy, a FIPA d’Or and the Royal Philharmonic Society Award.
In spite of the mixed reception accorded to her first production at the National Theatre, Lloyd nonetheless returned to direct productions of The Way of the World, Pericles, What the Butler Saw, The Prime of Miss Jean Brodie and The Duchess of Malfi, which were well-received. She directed an award-winning production of Boston Marriage at London's Donmar Warehouse in 2001. Other recent work includes Schiller's Mary Stuart for the Donmar, which will transfer to Broadway in 2008.
In 1999 Lloyd was offered the chance to direct the ABBA musical Mamma Mia!, which became a hit, not only in the West End and on Broadway, but world-wide. She directed the 2008 big screen adaptation, which marked her feature debut.