This question has been answered on math.SE (as pointed out by Joel David Hamkins). With a reference to Lambda-Calculus and Combinators in the 20th Century by Felice Cardone and J. Roger Hindley, Handbook of the History of Logic Volume 5, 2009, Pages 723–817, it is stated that “$\lambda x$” comes from “$\hat x$.”
A preprint of that article is available online, here is a quote from it:
By the way, why did Church choose the notation “$\lambda$”? In [A. Church, 7 July 1964. Unpublished letter to Harald Dickson, §2] he stated clearly that it came from the notation “$\hat x$” used for class-abstraction by Whitehead and Russell, by first modifying “$\hat x$” to “$\wedge x$” to distinguish function-abstraction from class-abstraction, and then changing “$\wedge$” to “$\lambda$” for ease of printing. This origin was also reported in [J. B. Rosser. Highlights of the history of the lambda calculus. Annals of the History of Computing, 6:337—349, 1984, p.338]. On the other hand, in his later years Church told two enquirers that the choice was more accidental: a symbol was needed and “$\lambda$” just happened to be chosen.