As a student at St Andrews University he was placed in the Honours List of all his classes (which included Greek, Humanity, Rhetoric and English Literature, Moral Philosophy and Political Economy) obtaining first place in Mathematics, Natural Philosophy, Chemistry, Logic and Metaphysics, Anatomy and Physiology. Among his prizes were three for Mathematics, two for Chemistry and one for Mental Philosophy.
Mr Lawson's association with the University continued when he became a member of the Mathematics staff. Later he held University appointments as a Member of the Scottish Universities Joint Board, and as an Examiner in Mathematics, Dynamics and Physics; while for many years he represented the General Council as Assessor on the University Court.
Prior to his appointment to the Rectorship of Waid Academy in 1904, Mr Lawson served as a Master in George Watson's College, Edinburgh, and as Rector of Selkirk High School.
As a teacher his work was mostly in the Department of Mathematics, and he made a special study of the teaching of this subject. By his numerous contributions to Educational Journals on mathematical subjects, his papers read before various societies, and by his "School Geometry," he had a marked influence on the improvement of the teaching of Geometry in our schools. Mr Lawson's life work may be said to have been done in Anstruther, where for twenty-seven years he guided the destiny of Waid Academy with "conspicuous fidelity and distinguished scholarship.+ On the occasion of his retiral in 1931 an enthusiastic gathering of pupils, members of the staff and of the public showed the esteem and goodwill in which he was held during his long residence in East Fife by presenting him with several handsome gifts.
Mr Lawson took a keen interest in public affairs and served on Anstruther Easter Town Council, Parish Council, and as a Murray Library Trustee. His regard and admiration for the fishermen found in the expression in the English Medal which he founded and which bears the inscription "English Medal in honour of the splendid services rendered to our Country and Allies during the Great War 1914-19 by the brave fishermen and seamen of the Waid Coast."
Mr Lawson became a member of the Edinburgh Mathematical Society in 1897 and was a member of the first Mathematical Colloquium in 1913, but it was only when he came to reside in Edinburgh in 1932 that he was able to take an active part in the work of the Society. He was elected President in 1937 and presided with much acceptance, at the meetings of the Colloquium held at St Andrews in 1938.