Appleby was born at Deseronto, Ontario in 1895. His medical training at Queen's University, Kingston, Ontario was interrupted by service at No 7 Canadian General Hospital during the war of 1914-18; he graduated in 1919 winning the gold medal of his year. He made postgraduate studies in England and Canada, taking the Fellowship in 1921. He settled at Vancouver, British Columbia in 1924 and practised there till 1968; he was on the staff of St Paul's Hospital throughout his career, and ultimately surgeon-in-chief. Appleby was active in medical institutions and wrote often in surgical journals. He was president of the International College of Surgeons at Chicago in 1962-64, and was elected a Fellow of the Royal College of Physicians and Surgeons of Canada at Ottawa. He was a keen racing man, who bred and raced his own horses. He died at Vancouver on 10 April 1970 aged 75, survived by his daughter and three sons; two of his sons, Lyon Henry (Junior) and Kenneth, were in medical practice in British Columbia.