Launceston Elliott was born in India. His family was an established part of the British aristocracy with Lord Minto being head of the family which had strong connections with India. The 4th Earl Minto served as Viceroy of India (1905-1910). Launceston Elliott was the grandson of Sir Charles Elliot, the onetime governor of St. Helena, and his father served as magistrate with the Indian Civil Service.
In 1887, Elliot's father gave up his post in India and took his family to England where he began farming in Essex. The 13-year-old Launceston, an exceptionally well-built youth, who was seeing England for the first time, immediately came under the influence of the great Eugen Sandow and soon developed into an unusually talented lifter. In January 1891, aged only 16, he performed creditably at what is now recognized as the first British Championships held at the fashionable Cafe Monico in Piccadilly, London. Three years later he was the winner of the championships at the Royal Aquarium, Westminster.
Continuing success encouraged the 21-year-old Elliot to travel to Athens for the first modern Olympic Games. At the time, there were no internationally accepted rules or classifications for weightlifting and the 1896 Olympics added further to the huge variety of classes contested on the contemporary scene. The two-handed lift came first on the program and, after a long drawn out contest, Viggo Jensen of Denmark and Elliot had both lifted 110 kg., but Prince George awarded the Dane first place for having done so in better style. Jensen's lift was accomplished with a superb clean lift whereas Elliot had certainly encountered difficulty. By contrast, the one-handed event was a short, sharp event. Elliot declined Prince George's courteous offer of a rest break but he asked that he might this time lift after Jensen, as in the two-handed event the Dane had the advantage of lifting after Elliot. The request was granted although the order of lifting was not to have a material effect on the result. Elliot raised 71.0 kg. without difficulty whereas Jensen, who had injured his shoulder trying to raise 112.5 kg. in the two-handed event, could only manage 57.2 kg. and Britain's first Olympic champion was crowned.
Since his victory in Athens, he had set four new records at the 1899 Amateur Championships and, as a prominent figure on the British weightlifting scene, his financial success was virtually assured. In 1905 he turned to professional. After his retirement Elliott carried on farming in England for a few years before settling in Melbourne in 1923. He died of cancer of the spine on 8 August 1930.