It depicts the scientist Sir Humphry Davy, president of the Royal Society.
It shows Davy in the stance of a swagger portrait dressed in fashionable Regency era style.
Lawrence was Britain's leading portraitist and had succeeded Benjamin West as president of the Royal Academy the previous year.
Lawrence and Davy were friends and in the year of the painting the two presidents took part together in the Coronation of George IV at Westminster Abbey, representing the arts and sciences.
The copy in the National Portrait Gallery was done by Lawrence's studio, likely by Richard Evans.