He was the second son of Johnson Lawson, dean of Battle, Sussex, and Elizabeth, daughter of Henry Wright of Bath, Somerset, he was born at Greenwich on 23 March 1774.

[1] Lawson had offered in December 1851 his astronomical apparatus, with 1000 guineas, to the town of Nottingham, on condition of money enough being raised to build and endow an observatory.

His eleven-foot telescope was later presented to the Royal Hospital School at Greenwich, the five-foot to William Garrow Lettsom, and his meteorological appliances to Edward Joseph Lowe.

[1] Lawson observed an occultation of Saturn on 8 May 1832, Johann Gottfried Galle's first comet in December 1839 and January 1840, and recorded the falling stars of 12–13 November 1841.

[1] The Society of Arts, of which he was a member, voted Lawson a silver medal for the invention of an observing-chair called "Reclinea", and awarded him a prize for a new thermometer-stand, described before the British Association in 1845.

He made communications to the British Association in 1846 and 1847 on solar telescopic work, and published in 1853 accounts of his designs for a "lifting apparatus" for invalids, and of a "surgical transferrer".