No, computation is a mathematical discipline; the lambda calculus is one way of thinking about computation (I won't say it's the best, but it's a way) which is part of that discipline; C simply … isn't.
Common Lisp, of course, is a hell of a lot more than just the lambda calculus, but it's also a hell of a lot better a language than is C.
From a pragmatic perspective computing is just "a lot of programs".
It's not what "should be" -- it's what it is.