In 2010 Lethbridge was discovered to be the father of Claire Clairmont. It appears that Lethbridge had an affair with Mary Jane Vial Clairmont, who gave birth to a daughter on 27 April 1798 in Brislington, near Bristol. Births outside marriage then carried great stigma for the mother and child. Correspondence, including lawyers' letters, show that, after some pressure, he acknowledged paternity and made a financial settlement. Nonetheless, the child did not bear his name: the mother identified him as a "Charles Clairmont", adopting the name Clairmont for herself and both her children, to disguise their illegitimacy. A few years later, she married the writer and philosopher William Godwin, so Lethbridge's daughter grew up in a literary household with a blended family, including Godwin's stepdaughter (Fanny Imlay) and daughter by his late wife Mary Wollstonecraft. When the younger of these, Mary, eloped with the poet Percy Bysshe Shelley, Claire Clairmont accompanied them on their flight to Europe. Through Shelley, she formed an attachment to Lord Byron, and bore him a daughter. Thus Lethbridge was the grandfather of Allegra Byron.