He was educated at Hanson Boys' Grammar School, Bradford, and entered the theatre in his late teens, appearing on both the British and American stage throughout his career.

He made his film début in East Lynne on the Western Front (1931) and appeared in supporting roles until he took the lead in The Terror (1938).

He also had memorable leading roles in Pastor Hall (1940), as a German village clergyman who denounces the new Nazi regime in 1934; Tower of Terror (1941) as the wild-eyed maniacal lighthouse keeper Wolfe Kristen; and the title role in The Great Mr. Handel (1942), a biopic of the 18th century composer, all three showing his broad range.

Despite this he still gave memorable performances such as Prince Andrei Bolkonsky's father in King Vidor's War and Peace (1956), Ed in Hell Drivers (1957) and Uncle Nat in Room at the Top (1958), filmed in Lawson's home town of Bradford.

The 1960s saw something of a career resurgence, beginning with his turn as Black George in Tony Richardson's Tom Jones (1963) and culminating in two of his most notable latter day performances: the decrepit butler Peacock in The Wrong Box and the Dormouse in Jonathan Miller's television adaptation of Alice in Wonderland (both 1966).