Googling a bit, it seems that McCarthy mentions this in "History of Lisp" [0], as a change from LISP 1 to LISP 1.5:

> In modern terminology, lexical scoping was wanted, and dynamic scoping was obtained. I must confess that I regarded this difficulty as just a bug and expressed confidence that Steve Russell would soon fix it. He did fix it but by inventing the so-called FUNARG device that took the lexical environment along with the functional argument. Similar difficulties later showed up in Algol 60, and Russell's turned out to be one of the more comprehensive solutions to the problem. While it worked well in the interpreter, comprehensiveness and speed seem to be opposed in compiled code, and this led to a succession of compromises. Unfortunately, time did not permit writing an appendix giving the history of the problem, and the interested reader is referred to (Moses 1970) as a place to start. (David Park tells me that Patrick Fischer also had a hand in developing the FUNARG device).

So I guess closures had been invented at least by 1962 (when the LISP 1.5 manual was published), but were not widely used because of performance considerations?

[0] http://www-formal.stanford.edu/jmc/history/lisp/node4.html