Airdrie, Lanarkshire born inside right Laurie Conwell began his football career with Arthurlie and joined Scottish First Division club Aberdeen in March 1934. Conwell scored a hat-trick on his Scottish Junior International debut against England at Dens Park, Dundee early the next month, making his League debut for Aberdeen in a win over Falkirk at Pittodrie that August. Conwell scored once in 7 appearances for Aberdeen before signing for Irish League club Portadown in May 1935.
His spell in Irish football was brief and he was signed by Second Division club West Ham United that October, making his Football League debut against Bradford City the same month, and he played 6 matches over the next month, scoring in a win over Hull City, before losing his place in early December.
He made just two more appearances for West Ham in 1936-37 before transferring to Coventry City in March 1937, where he played only two matches for The Sky Blues either side of New Year 1937-38. However he was not retained and left professional football in the 1938 close season, joining non league Hinckley United.