L'Amy was born on 8 July 1772 the son of Agnes (née) Hamilton and John Ramsay L'Amy of Dunkenny, Forfarshire. His older sister was the Scottish poet Agnes Lyon. He studied law and qualified as an advocate in 1794.
In the 1820s he was living at 27 Northumberland Street next to the "father of phrenology" and fellow-lawyer, George Combe, at 25 Northumberland Street. Combe may have introduced L'Amy to phrenological thinking.
He died on 15 January 1854 in Edinburgh and is buried with his wife and family in Greyfriars Kirkyard. The grave stands at the top end of the western extension facing the eastern gate into George Heriot's School.
In 1811 he married Mary Carson (d.1835). Their children included John Ramsay L'Amy (1813-1892).
- Matthew, H. C. G.; Harrison, B., eds. (23 September 2004), "The Oxford Dictionary of National Biography", The Oxford Dictionary of National Biography, Oxford: Oxford University Press, pp. ref:odnb/17273, doi:10.1093/ref:odnb/17273, retrieved 14 July 2021
- Edinburgh and Leith Post Office Directory 1830-31
- The Edinburgh New Philosophical Journal, volume 31 (1841)
- Edinburgh Post Office Directory 1852