The Scotsman, who won three caps for his country, was Bill Shankly's first-choice keeper during the 1960s.
Lawrence signed professionally for Liverpool in October 1957, just months after his 17th birthday.
The Ayrshire-born stopper made his Reds debut in 1962, five years after signing, and became a pivotal member of Shankly's side.
During Lawrence's time as first-team keeper at Anfield, the Reds won the First Division title twice and claimed the FA Cup for the first time.
After leaving Liverpool in 1971, Lawrence played out the remainder of his career at Tranmere Rovers and non-league side Chorley before working as a factory quality controller.