Lawrence was born in Kensington, London and was a pupil at Christopher Wren School where he was spotted by Southampton's London scouting network, joining The Saints as a trainee in August 1979. He made his debut in a League Cup match against Chelsea on 6 October 1981 replacing Nick Holmes. He made his first appearance in the starting line-up on 17 October, replacing Mick Channon in a league game against Notts County. According to Holley & Chalk's The Alphabet of the Saints, he "soon brought added meaning to the wordunpredictable". He was "full of strong surging runs" and "would, when remembering to take the ball with him, completely perplex opposing defenders and cause havoc in the penalty area". In his first period at The Dell, Southampton had an abundance of strikers, including Channon and Steve Moran, together with Kevin Keegan, Steve Williams and David Armstrong in midfield, so his chances were limited. He spent the end of the 1981–82 seasonon loan at Oxford United and, after returning to Southampton for the start of the following season, he moved permanently to Oxford in November 1982. After two years with Oxford, he was rather surprisingly re-signed by the Saints' newly appointed manager, Chris Nicholl. Again, Lawrence was in competition with several strikers including Moran, Joe Jordan, Alan Curtis and Danny Wallace. Lawrence knuckled down and, always with a smile on his face, set out to try to make his second spell more productive than the first. The 1986–87 season was his most successful with Southampton, making 36 League appearances and was the club's second-best scorer for the season with eight goals. It was somewhat of a surprise to the Saints fans, therefore, when he was sold to Millwall for £160,000 in July 1987, although by now Matt Le Tissier and Alan Shearer were coming up through the ranks and were pushing for promotion to the first team. In his two periods with the Saints he made 104 appearances in all competitions, scoring 15 goals. In his first season at Millwall, he helped them win the Football League Division 2 championship, and then spent the 1988–89 season with them in the First Division. He then spent three years at Bournemouth before spending the summer of 1992 in Finland with Mikkelin Palloilijat. In 1993, he made 14 appearances for Portsmouth, all from the substitutes' bench. He finished his playing career with a spell in Malta, playing with Hibernians F.C. where he won two consecutive titles, followed by lower-league football. Since retiring from playing professionally, he has continued to turn out in veterans' matches as well as earning a living as a player's agent.
Throughout his career, he was affectionately known by the nickname "Chicken George", after the character in the TV seriesRoots which was being aired on British television at the time he started his career.
