Lawson was born in Crieff, Perthshire, the son of Phyllis Neno (née Stamper), who sold sweets, and Laurence Lawson, a watchmaker and Glasgow native. Lawson was educated at Crieff Primary School (then called Crieff Public School). After the 11 plus examination, he went on to Morrison's Academy, which at that time took non-fee-paying pupils as well as fee-paying day pupils and boarders. Also, he attended the Royal Scottish Academy of Music and Drama. His sister, Carol Diane McGregor, is a retired teacher who still lives in Perthshire. She is the mother of actor Ewan McGregor who played Obi Wan Kenobi in the Star Wars prequel trilogy. In 1979, Lawson had a child, Jamie, with actress Diane Fletcher, with whom he had a seven-year relationship after meeting in a stage production of Twelfth Night. He met his wife, Sheila Gish, on the set of the 1985 film That Uncertain Feeling. They lived together for nearly 20 years before marrying in March 2004 (Antigua); she died of cancer a year later (9 March 2005). Her daughter from a previous marriage, Lou Gish, also succumbed to cancer in 2006.

Lawson began his acting career with a small role in a 1969 stage production of The Metamorphosis in London's West End. and has since starred in television dramas such as The Merchant of Venice (1973) opposite Sir Laurence Olivier as Shylock, Rock Follies (1976) and Dead Head (1986). He played X-wing pilot Wedge Antilles in all three original Star Wars movies, and later reprised the role, in voiceover form, for the Nintendo GameCube game Star Wars: Rogue Squadron 2. He has appeared often on the West End stage, most notably in 527-show 1983-1984 run of the musical Mr. Cinders at the Fortune Theatre. In 1999, he directed a production of "Little Malcolm & His Struggle Against the Eunuchs" - first at the Hampstead Theatre before transferring to the Comedy Theatre in London's West End. The production starred his nephew Ewan McGregor in the lead role of Malcolm Scrawdyke

He appeared on an episode of "Loose Ends" hosted by Ned Sherrin on BBC Radio 4 (10 December 2005), during which his cell phone rang. In 2005, he played the leading role of John Jarndyce in the critically acclaimed BBC adaptation of Charles Dickens' Bleak House, receiving an Emmy nomination. As a joke, George Lucas offered him the role of Raymus Antilles (unrelated to Wedge) in Star Wars Episode III: Revenge of the Sith, which Lawson declined.

In 2007, he portrayed Peter Syme in the BBC One drama serial Jekyll, a modern version of The Strange Case of Dr Jekyll and Mr Hyde. Lawson also appeared as Captain "Dreadnought" Foster in one of ITV's dramatisations of C.S. Forester's Hornblower - The second episode in the series, "The Examination for Lieutenant". He appeared in the BBC adaptation of Robin Hood, in episode six, For England!, in which he played the Sheriff of Winchester. He also appeared in the West End playing the character of Georges in the revival of the musical hit La Cage Aux Folles (closed in Jan 2010). No stranger to musical theatre Lawson previously starred in the London revival of Pal Joey earning rave reviews.

He starred as the lead in 'Above Their Station' a new sitcom for the BBC written by Rhys Thomas about Community Support Officers; it was made as a pilot but never commissioned only being shown as a one-off special. Lawson appeared alongside Academy Award nominated actress Helena Bonham Carter the BBC Four movie based on the life of Enid Blyton, playing Kenneth Darrell Waters, a London surgeon who becomes Blyton's second husband. In July 2009 Lawson appeared as Alexander Fleming in a BBC Four drama called 'Breaking the Mould: The Story of Penicillin' alongside Dominic West from The Wire.

Anton Rodgers (1979) · Denis Quilley (1980) · Michael Crawford (1981) · Roy Hudd (1982) · Denis Lawson (1983) · Paul Clarkson (1984) · Robert Lindsay (1985) · Michael Crawford (1986) · John Bardon and Emil Wolk (1987) · Con O'Neill (1988) · Jonathan Pryce (1989) · Philip Quast (1991) · Alan Bennett (1992) · Henry Goodman (1993) · Alun Armstrong (1994) · John Gordon Sinclair (1995) · Adrian Lester (1996) · Robert Lindsay (1997) · Philip Quast (1998) · Jody Abrahams / Loukmaan Adams / Mandisa Bardill / Junaid Booysen / Salie Daniels / Alistair Izobell (1999) · Simon Russell Beale (2000) · Daniel Evans (2001) · Philip Quast (2002) · Alex Jennings (2003) · David Bedella (2004) · Nathan Lane (2005) · James Lomas / George Maguire / Liam Mower (2006) · Daniel Evans (2007) · Michael Ball (2008) · Douglas Hodge (2009) · Aneurin Barnard (2010)