Following in the footsteps of brother Billy Cook, Lawrence first came to notice playing for Penwortham Cricket Club.
For most of the time he was not a regular member of the senior eleven as many bowlers competed for two or three places, but near its end in his mid-thirties Cook bowled so well that some expected him to be chosen for the difficult 1920/1921 Ashes tour.
Nonetheless, shrewd judges are unanimous that Cook was not the bowler for Test matches against a formidable batting side on rock-hard pitches.
Lawrence emerged as a bowler of fast-medium pace, possibly meant to substitute for Walter Brearley who was then engaged in one of his many disputes with the Lancashire committee.
Cook indeed bowled so well early that season that Lancashire seemed to have found an excellent pace bowler when Brearley could not play.
However, he was felt impossible to fit in when that fast bowler was free from business and on returning to the side he did not maintain his early season form, nor did he do anything of note against the top counties.
Although he did not have the honour of representing the Players or touring Australia, Cook would no doubt have been chosen as a Cricketer of the Year by Wisden but for the special portrait of Pelham Warner to commemorate Middlesex's Championship win.
In the dry summer of 1921, Cook showed himself to be one of the most tireless and consistent workhorses in county cricket, even if no selector thought he had enough sting to be a Test match bowler.