20.1.1807 Durham at Joseph Johnson's / 22.4.1808 Lamb (Durham) at Coleridge's lecture
Unlikely to have been Shute Barrington (DNB 1734-1826) bishop of Durham - and Godwin would have probably added at least a Bp if it had been. The brackets at Coleridge's lecture could mean that this was a topic rather than a person. No Durhams in Lamb or Coleridge letter indexes. I found nobody in Watt or Allibone the usual sources for authors who were often the guests at Johnson's. Also no Durhams in Holdens 1811 court section, six in trades (see work notes below). Perhaps one of the sons of Thomas Durham bookseller of 34 Cockspur-st (died 1798) and his wife Lilly (died 1800) who left no wills but two of their sons went to Cambridge. William Alexander Campbell Durham (1776-1857) was chaplain at St Pauls school from 1806. James George Durham (1778-1832) won the Norrisian prize at Cambridge in 1804 for his essay on "The providence of god". The third son Robert Keith Archibald Durham (1777-1843) married Sarah Rotton in 1805 and his will PCC 1843 described him as a cutler.

Work notes: 
Holderns 1811: J Durham carpenter 6 Mill-st, Hanover-sq / John Durham upholsterer 23 Chienes-st / John Durham surgeon Enfield / Joseph Durham butcher Lower Shadwell Dock / Samuel Durham wine merchant 9 Gt Alie-st Goodmans-fields will PCC 19.11.1811 / William Durham haircutter 17 Bury-st St James voted 1818 Burdett & Romilly