Ah, ok, I find nothing to disagree with there. Looking back up the conversation, I see that I was responding to the word "behavior". Specifically, bigjeff5 said:

In other words, the same Lisp code will result in slightly different behavior on a Mac than it would on a Linux machine.

To which you responded:

If Lisp behaves differently from the mathematical ideal on any machine, that means the machine is incapable of supplying said turing machine.

So it comes down to: does the "behaviour" of a Lisp implementation include anything besides the output? Which effectively comes down to what question we're trying to answer about Lisp, or computation, or etc.

The original question was about whether a Lisp machine needs to include abstractions for the substrate it's running on. The most direct answer is "No, because the specification doesn't mention anything about the substrate." More generally, if a program needs introspection it can do it with quine trickery, or more realistically just use a system call.

Bigjeff5 responded by pointing out that the choice of substrate can determine whether or not the Lisp implementation is useful to anybody. This is of course correct, but this is a separate issue from whether or not the Lisp abstraction needs to include anything about its own substrate; a Lisp can be fast or slow, useful or useless, regardless of whether or not its internal abstractions include a reference to or description of the device it is running on.