The problem is all of this relies on a representation of the data structure you're manipulating. What exactly is the structure that a Lisp machine is manipulating?
The basis of Lisp is the Lambda Calculus, and a generalization of that gets you term rewriting. Both the basis and the generalization of Lisp admit to requiring a tree (or a graph, in the case of Cons-cells) to get on with the computations, because that's the "state" that you're working with.
The problem is that while these things in the minds of humans are pretty easy to work with, implementing them physically has you rely on things like the RAM model, which, while pretty far away from the Turing Machine, still has machine-like qualities.
That's my argument. We can't really build "Lisp Machines", we can build "Random Access Machines with Lisp Interfaces", because there's no physically implementable version of a tree or graph memory outside of linking randomly-accessible cells.