He entered Bootham School in York in 1823 and fell under the dual influences of pacifist Quaker beliefs and, under master J. Edmund Clark, science, in particular, meteorology. In 1898 he attended Durham College of Science, to study mathematics, physics, chemistry, zoology and botany, before graduating from King's College, Cambridge with a first-class degree in the Natural Science Tripos in 1903.
Richarson's early working life reflected his eclectic interests:
Richarson's interest in meteorology led him to propose a scheme for weather forecasting by solution of differential equations, the method used today, though, when he published Weather Prediction by Numerical Process in 1922, suitable fast computing was unavailable. He, somewhat eccentrically, envisaged bands of messengers on motor-cycles cruising the Royal Albert Hall to communicate arithmetical results between banks of clerks in order to obtain the necessary numerical solutions. He was also interested in atmospheric turbulence and performed many terrestrial experiments. The Richardson number, a dimensionless parameter in the theory of turbulence is named for him. He famously summarised the field in the parody:
Big whorls have little whorls that feed on their velocity, and little whorls have smaller whorls and so on to viscosity.
He also attempted to apply his mathematical skills in the service of his pacifist principles, in particular in understanding the roots of international conflict. He formed the theory that the propensity for war between two nations was a function of the length of their common border. In Arms and Insecurity (1949), and Statistics of Deadly Quarrels (1950), he sought to quantify this effect. In collecting data, he realised that there was considerable variation in the various gazetted lengths of international borders. For example, that between Spain and Portugal was variously quoted as 987 or 1214 km while that between The Netherlands and Belgium as 380 or 449 km. This led Richardson to the, rather obvious, realisation that the measured length of a line depends on the length of the 'ruler' used to measure it. However, further consideration of this idea led him to the concept of a line, so 'wriggly' that it fills a plane, a key step in the development of the mathematics of fractals.
Richardson died in Kilmun, Argyll, Scotland.