Lindsay's early work was mainly in theatre. One of his first London stage roles saw him play the King of France in King Lear at the Royal Court Theatre, with Tom Wilkinson as Lear and Andy Serkis as the Fool. At a weekly Monday night poker game organised by the actor Samuel West, Lindsay was asked by Patrick Marber to attend a week's improvisational workshop of a play he was devising about poker. This became Dealer's Choice, which premiered at the National Theatre in February 1995 with Lindsay as Mugsy and Ray Winstone and Phil Daniels among the original cast. The play transferred to the Vaudeville Theatre, and won that year's Evening Standard Award for Best Comedy and Writers' Guild Award for Best Play. Other theatre work includes: Max in The Real Thing by Tom Stoppard which won three Tonys on Broadway in 2000; Ariel in the 2004 Olivier award-winning National Theatre production of Martin McDonagh's The Pillowman, with Jim Broadbent and David Tennant; Nathan Detroit in Michael Grandage's Guys and Dolls at the Piccadilly Theatre in 2005, and Charlie Maggs in Sucker Punch by Roy Williams at the Royal Court in 2010. Lindsay has appeared in five plays at the Almeida Theatre, including as Lenny in Harold Pinter's The Homecoming with Ken Cranham and Danny Dyer in 2009 and as Moe Axelrod alongside Stockard Channing and Jodie Whittaker in Awake and Sing by Clifford Odets, for which he was nominated for Best Supporting Actor in the 2008 Whatsonstage Awards.

Lindsay has appeared in many regular series, including: Spooks, Silent Witness, Waking the Dead, Midsomer Murders, New Tricks and Between the Lines. He played Odo Stevens in the 1997 Channel 4 adaptation of A Dance to the Music of Time; Ewan McGregor's boss Ron Baker in the film Rogue Trader; the Jewish terrorist Levi in Rome; Sheriff Johnny Behan in the BBC's Gunfight at the O.K. Corral; Lt Col Mervyn Gonin in the BAFTA nominated The Relief of Belsen with Iain Glen; and opposite Jack Dee in Simon Nye's fairground comedy Tunnel of Love. He has worked with Steve Coogan on Alan Partridge, with Armando Iannucci on the Armando Iannucci Shows, with Jennifer Saunders in two series of Jam and Jerusalem, and again with Chris Morris on Brass Eye.

Lindsay won the 2011 Whatsonstage Award for Best Supporting Actor as Dr Harry Hyman in Arthur Miller's Broken Glass at the Tricycle Theatre. On 27 February 2012, he finished playing the title role in the original West End production of Shrek the Musical, which opened at the Theatre Royal, Drury Lane on 14 June 2011 and for which he was nominated for 2012 Laurence Olivier and Whatsonstage.com Awards for Best Actor in a Musical. Later theatre work includes playing Bolingbroke opposite David Tennant in the RSC production of Richard II at Stratford and the Barbican; and Jack McCracken in the National Theatre revival of the Alan Ayckbourn play A Small Family Business in the Olivier theatre.