The story
A place name truncated from a great variety of predecessors, the place having been formerly known as Laxington, Lexington, Lexinton, and Lessington. The earliest attestations of the place name are found in the Domesday Book variously as Laxintone and Lexingtune; these Domesday forms derive from the Anglo-Saxon Leaxingatūn, from the Anglo Saxon personal name Leaxa + -ing (“belonging to”) + tun (“settlement”), so meaning "farmstead or estate of the people of a man called Leaxa".
Etymology from Wiktionary, CC BY-SA 4.0.