This question has been answered [on math.SE](http://math.stackexchange.com/a/64469/413) (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](http://www.users.waitrose.com/~hindley/SomePapers_PDFs/2006Car,HistlamReprt.pdf), 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 Unpublished letter to Harald Dickson, §2]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.