I have seen two histories, one which implies the mutation was controlled by Church the other which implies it was accidental.
Both agree that Church based his original lambda calculus notation on Russell and Whitehead's principia mathematica (Church's work in general drew much from it) which used
^f(x) to denote a function whose application would result in f(x). Church modified it too ^x.f(x) for succintness.
But the type setter, like this forum could not put the circumflex on top of the x so it became ^x.f(x), here is where the story diverges. Some say this was mistaken for Λ where it mutated to λ under another typesetter.
The other story, which is the one I prefer states that after finding out there was no typesetting which allowed the circumflex to be on top Church decided to move it to the left but use Λ (capital lambda) instead. He decided it looked too much like the conjunction symbol and so made it the lower case lambda. Hence λx.f(x).