I think you've missed the point of OPs question - he's not trying to argue that lisp isn't useful over Lambda Calculus from a practical perspective, but asking how both relate to the "fundamentals of computing" perspective.
So to answer your question, nothing (in this context), because the Turing machine is a more useful model for thinking about computation itself.
Perhaps the same might apply to lisp / lambda calculus, although I suspect the answer here is that it's just a lot harder to right a self-interpreter in lambda calc.
> So to answer your question, nothing (in this context), because the Turing machine is a more useful model for thinking about computation itself.
This isn't obvious to me. It seems to me that a TM is more useful for thinking about computation from an operational perspective. But this isn't the only, or arguably even the most effective, way to think about computation. The lambda calculus is much more useful for thinking about computation from a denotational perspective.
I agree completely, and didn't mean to compare the Turing machine to Lambda calculus, only to the C language (it made more sense before the context above was deleted).
So to answer your question, nothing (in this context), because the Turing machine is a more useful model for thinking about computation itself.
Perhaps the same might apply to lisp / lambda calculus, although I suspect the answer here is that it's just a lot harder to right a self-interpreter in lambda calc.