What the author was saying about TCO was that, based on the fact that all our machines today use stacks, and not wanting to have programs that break(!), any implementations of lambda calculus on these machines must have TCO to allow as much of the lambda calculus as possible to be available in the programming language, lest you reject otherwise correct programs.
But make no mistake, Lisp[2] and functional programming languages ARE based on the lambda calculus. The article really did hit the nail on the head.
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[1] "Lisp was originally created as a practical mathematical notation for computer programs, based on Alonzo Church's lambda calculus."
-- Wikipedia (http://en.wikipedia.org/wiki/Lisp_%28programming_language%29)
(and lots of other sources agree with this)
[2] Sorry to say it, but Lisp isn't the center of the Universe. It's a cool trick, but it isn't that great.