Born in Newcastle-upon-Tyne, she was educated at Lady Margaret Hall (BA) and at St Antony's College (DPhil). After teaching at Queen Mary's College and holding a Fellowship at the Woodrow Wilson International Center for Scholars, she was in 1977 appointed Fellow and Tutor in Modern History at Lady Margaret Hall. She was Vice-Principal 1992–97 and became Principal in 2002. She retired on 30 September 2015.
Lannon is a Fellow of the Royal Historical Society. In 2006, she was a visiting scholar at the Australian National University Research School of Social Sciences and Australian Consortium for Social and Political Research Incorporated Centre for Social Research.
- Frances Lannon, Catholic Bilbao from Restoration to Republic: a Selective Study of Educational Institutions, 1876–1931 (University of Oxford DPhil thesis 1975)
- Frances Lannon, Privilege, Persecution, and Prophecy: the Catholic Church in Spain, 1875–1975 (Oxford: Clarendon Press, 1987)
- Frances Lannon and Paul Preston (editors) Elites and Power in Twentieth-Century Spain: Essays in Honour of Sir Raymond Carr (Oxford: Clarendon Press, 1990)
- Frances Lannon, 'Women and Images of Women in the Spanish Civil War', Transactions of the Royal Historical Society 6th series, 1 (1991), 213–228
- Frances Lannon, 1898 and the Politics of Catholic Identity in Spain, in Austen Ivereigh, ed., The Politics of Religion in an Age of Revival (London: Institute of Latin American Studies, 2000)
- Frances Lannon, The Spanish Civil War, 1936–1939 (Oxford: Osprey, 2002)
- Frances Lannon, Lady Margaret Hall, Oxford: the First 125 Years, 1879–2004 (Oxford: Lady Margaret Hall, 2004)
- Profile at Debretts