We've been over this. Gödel's mu-recursive functions were a poor model of computation because it's completely unclear how to physically implement the arbitrary-function minimization operator. So people didn't see how to build a machine that calculates this way. Similarly, there's no clear way how to mechanize lambda calculus. Turing Machines, on the other hand, were instantly obviously mechanizable. It was clear that…
> Similarly, there's no clear way how to mechanize lambda calculus. Is Lisp such a mechanization?
The famous Lisp Machines of the 1980s were reasonably traditional Von Neumann computers with nice features like tagged memory and optimized stacks.
Much closer to mechanizing lambda calculus, but still a bit Von Neumannish, is the SECD virtual machine for Lisp and friends: