Born in London on December 11, 1870, and educated at Birkbeck School, Clapton, he qualified as a Fellow of the Institute of Actuaries at the age of twenty-one. His exceptional ability was soon recognised and, when only twenty-three, he was appointed Assistant Actuary of the Alliance Assurance Company. In 1902 he became joint Actuary, and later Actuary, of that Company, and in 1905 was chosen for the principal post - Actuary and Secretary - of the Equitable Life Assurance Society. In 1913, when he came to Edinburgh as Manager and Actuary of the Scottish Widows' Fund, he held a world-wide reputation as one of the leading actuaries of the day.
It is not possible in a short memoir to describe Lidstone's work and achievements in any detail. Merely to compile a complete list of his writings would be a formidable task. They began when he was a student with a letter to the journal of the Institute of Actuaries suggesting an improvement in the textbook solution of an actuarial problem, and from that time until blindness overtook him towards the end of his life there was seldom a volume of the actuarial publications which did not contain at least one contribution from him. Much of his work took the form of notes and articles and it was always of the highest quality. The papers he presented for discussion by the profession were all submitted to the Institute of Actuaries before he came to Scotland, and the one which brought him fame was written in 1898 at the early age of twenty-seven. At that time the growing volume of endowment assurances was becoming a serious embarrassment to life offices at their periodical valuations, as the values depended not only on the age attained but on the term of years still to run to the maturity date. Lidstone suggested an ingenious approximate method whereby the work could be reduced to a mere fraction of that hitherto involved, and, what is more, an approximation so close as to be almost exact. The method is still used by most British life offices.
On coming to Edinburgh he received a warm welcome from the Faculty of Actuaries, of which he was elected a Fellow, and he was soon a valued member of its Council. He was its President from 1924 to 1926, and certainly one of its greatest Presidents. His exceptional ability and energy were devoted unsparingly to the interests of the Faculty, and he probably did more than any other in the past forty years to influence its destiny and guide its development on the scientific side, thereby earning the deep gratitude not only of the present generation of actuaries but of generations to come. He did much to strengthen that close association between the Faculty and the Mathematical Department of Edinburgh University which has been of such value to both. Although he never read a paper for discussion at the Faculty, he inspired papers by others, produced many valuable notes and contributed to numerous discussions. He was genuinely interested in the younger members, many of whom received much help and encouragement from him. His deep learning and wide knowledge were not confined to the actuarial field. He had a keen interest in law, and his purely mathematical attainments were considerable. He had the distinction of having his name given to a series, now known in mathematical analysis as the Lidstone series, by which a function is expressed in terms of its values at two points, and the corresponding derivatives of even order. The series is itself a particular case of very wide generalisations of the Everett interpolation formulae which he published in 1929. His eminence was recognised in 1925 when the University of Edinburgh conferred upon him the honorary degree of LL.D.
In 1929, on medical advice, he retired from the position of Manager and Actuary of the Scottish Widows' Fund and shortly afterwards was elected a Director. In the same year the Institute and Faculty jointly presented him with a gold medal in recognition of "his unique services to actuarial science" - a signal honour. He suffered an irreparable loss early in the war by the death of his wife after forty years of happy married life - a loss which was all but overwhelming at a time when his eyesight had begun to fail and his need of her care and attention was greater than ever. Those who knew her will always retain happy memories of Mrs Lidstone and her hospitality, friendliness, charm and humour. About this time Lidstone resigned from the General Claims Tribunal under the Compensation Defence Act of 1939, on which he had served since its formation, and a few years later, owing to the continued deterioration of his sight, he gave up his Directorships of the Scottish Widows' Fund and of the Royal Bank of Scotland, which he had also served.
Latterly he became completely blind - a severe trial for one who had for so long followed every detail of new work in actuarial subjects - but he bore his affliction with great fortitude, and in a remarkable way succeeded in keeping abreast of developments in the profession he had adorned.
He was a man of average height, but being of spare build looked taller, and his sharp features and penetrating eyes gave him an arresting appearance. His manner was austere and formal, disconcerting to those who did not know him well, but in fact forming a cloak for an intense shyness and diffidence.
He was deeply moved by music, of which he had an extensive knowledge, and he loved especially the classics and above all Wagnerian opera; towards the end he found solace in listening to some of his favourite music on the radio.
It is perhaps appropriate to conclude by saying of Lidstone, as he said of another eminent actuary, Sir George Francis Hardy who had been his tutor and later his close friend and with whom he had much in common: "He will always remain a brilliant example."
He was elected a Fellow of the Society in 1918, and served on the Council in the sessions 1919-22.