The story
Uncertain. Although current dictionaries all associate it with Charles Cochrane-Baillie, 2nd Baron Lamington, the earliest publication of this derivation is by John Hepworth in the Nation Review of July 1977. An earlier (1966) reference gives the cake but does not associate it with the Baron, suggesting the theory was not current in the 1960s. It has also been claimed that the name comes from Lamington, South Lanarkshire.
Etymology from Wiktionary, CC BY-SA 4.0.