Nicknamed "Henry" after the Australian poet, Lawson was a fast bowler for New South Wales (NSW) and Australia.

For a few seasons in the early 1980s, Lawson was Australia's leading fast bowler, but his career suffered from poor luck with injury.

He has broadcast for ABC Radio, Channel Nine and Foxsports, and contributed to The Sydney Morning Herald and other newspapers and magazines in various countries.

Lawson first came to notice in international cricket by bowling a series of bouncers during a brief spell against Geoff Boycott in a tour match between NSW and England in the 1978–79 season.

Chosen for nine preliminary ODIs in the World Series Cup, his total of nine wickets was not enough to earn him selection for the finals against the West Indies.

Lawson enjoyed a successful World Series Cup tournament, capturing 16 wickets at 15.80 in ten ODIs as Australia defeated New Zealand in the final.

In the third Test at Adelaide, he claimed 8/112 in a marathon spell on a batting-friendly pitch, then made 49 in the first innings but Australia lost the match, and eventually the series 1–3.

As Australia began rebuilding its team, Lawson was absent for most of the next three years, due to injuries and falling out of favour with the selectors and the captain Allan Border.

[9] Lawson recovered to make the 1989 tour of England, when his experience and guile contributed to a resurgence in Australia's performances.

Forming a potent pace bowling attack with Terry Alderman and Merv Hughes, Lawson finished with 29 wickets at 27.27 as Australia won back the Ashes with a crushing 4–0 victory.

His positive, aggressive captaincy influenced NSW colleagues and future Australian captains Mark Taylor and Steve Waugh.