The Lawrence family moved to North West England when Tommy was a child along with elder brother William (Billy) and younger sister Mary.

On leaving school he worked at Rylands wire factory and played for Croft Village Football Team, and then Warrington Town as an amateur.

His first clean-sheet came on 17 November, when Liverpool beat fellow promotion hopefuls Leyton Orient at Anfield 5–0, with Roger Hunt scoring a hat-trick.

Lawrence went on to retain the No.1 jersey that season making 35 appearances, including 6 ties in Liverpool's run to the FA Cup semi-final at Hillsborough.

[5] Lawrence held off the challenge of teenage keeper Ray Clemence when the youngster arrived from Scunthorpe United in 1967, but Liverpool had begun to decline as the team aged.

Though Lawrence was not the eldest, he was suddenly removed from the team in favour of Clemence after a 1–0 6th round FA Cup defeat at Watford in 1970; along with outfield players Ron Yeats and Ian St John.

Lawrence had to wait six years for his second and third caps, a 1–1 draw with West Germany in a 1970 World Cup qualifier and a 5–3 victory over Wales in a British Home Championship match.

[9][10] In February 2015, Lawrence was inadvertently interviewed in the street by BBC journalist Stuart Flinders, who was asking elderly people if they remembered the 1966–67 FA Cup Fifth Round game between Liverpool and Everton.