Lawrence is the son of Renaldo Lawrence who was drafted by the San Diego Clippers in the eighth round of the 1979 NBA Draft. He is also the nephew of David Lawrence who played in the British Basketball League for six seasons. He attended St. John the Baptist secondary school (SJB) in Woking, Surrey.
In Andrew's freshman season at the College of Charleston, he appeared in all thirty-four games, averaging 4.7 points per game. On 30 January 2010 Andrew scored a season-high thirteen points against Georgia Southern University.
Andrew appeared in all thirty-six games his sophomore season, including two starts. He averaged 5.8 points, 1.8 rebounds, and 1.7 assists per game. Andrew also led the team in total steals, with thirty-seven.
In his junior season, Andrew averaged 13.0 points, 5.5 assists, 2.9 rebounds, and 1.9 steals per game. On 2 February 2012 Andrew scored a career high 32 points in a double-overtime loss to Elon. He was also named to the All-Southern Conference second team.
As a senior Lawrence was chosen for a second-straight year in the Second team of the Southern Conference.
Following graduation Andrew Lawrence was selected as a member of the Washington Wizards 2013 NBA Summer League squad averaging 5.8ppg, 1.8apg and 2.5rpg.
In September 2013, he signed with KK Zadar of Croatia for the 2013–14 season.
After being inactive during one entire season due to an injury, in July 2015 he signed with Spanish Gipuzkoa Basket.
Andrew made his first appearance for the Great Britain national basketball team at the 2008 Under-18 Division B European Championship. In the tournament, Andrew averaged 12.5 points, 5.7 rebounds, and 4.5 assists per game. He also participated in the 2009 Under-20 Division B European Championship and the 2010 Under-20 European Championship. Andrew made his first senior appearance for the Great Britain national basketball team at the 2011 London Invitational Tournament. He averaged 7.5 points, 1.2 rebounds, and 1 assist per game during the tournament. Andrew also appeared in FIBA EuroBasket 2011, where he averaged 1 point, 0.7 rebounds, and 0.7 assists per game. On 5 July 2012 Andrew was named to the Great Britain Olympic Basketball Team. In an exhibition game against the United States, Lawrence recorded six points, three rebounds, and three assists.