Lumsden represented Jamaica in the Brandon Trophy on several occasions and also competed under the flag of the Commonwealth Caribbean in the Davis Cup. In 1966, the Davis Cup team of Lance Lumsden and Richard Russell defeated Venezuela by 3-2, the first time that the Commonwealth Caribbean had won a Davis Cup tie. In the following Davis Cup tie against the United States at the St Andrew Club in Kingston, Lance Lumsden and Richard Russell scored a famous victory on May 21, 1966, when they won the doubles match against the top-ranked American duo of Arthur Ashe and Charlie Pasarell, winning in five sets 6-4, 7-9, 14-12, 4-6, 6-4. This was the first time that the Commonwealth Caribbean had won a Davis Cup match against the United States. Although the United States won the tie by 4-1, this doubles victory by Lumsden and Russell in May 1966 is still regarded as one of the finest hours in the history of tennis in Jamaica and the Caribbean.
After retiring from tennis, Lance settled in Vienna, Austria, where he married and raised a family. He leaves sons Joris, Marco and Robin (Robin Lumsden, current honorary consul of Jamaica to Austria).
According to his nephew Richard Lumsden, the former Davis Cup player had been undergoing treatment for cancer when he died at the age of 71.
A service of thanksgiving for the life of Lance Lumsden will be held on Friday, July 15, 2011 at the St Andrew Parish Church at 1 p.m.