Launceston Elliot was born in Hubli, Karnataka, British India. He was conveived in Launceston, Tasmania, Australia for which he was named after. His family was an established part of the Scottish 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 Elliot was the grandson of Sir Charles Elliot, the onetime governor of Saint Helena, and his father Gilbert Wray Elliot served as magistrate with the Indian Civil Service.

Launceston Elliot died of cancer of the spine at the age of 56 in Melbourne, Australia. He is buried in Fawkner Cemetery in Melbourne, Australia.