> Did you even read the piece by McCarty?
Sure, the paper was more a side-effect of their work on LISP 1 and the mathematical ideas were developed at the end of the first phase of the development & implementation of LISP.
> He talks about how it was meant as an alternative to the computational models based on turing machines in addition to a symbolic computation tool for AI and therefore used side effects for convenience but also tried to keep mathematical properties, like referential transparency.
The programming language LISP 1 had SET, SETQ, control flow via GOTO, setting of slots of cons cells, destructive operations for list processing, destructive property list operations, ...
LISP was an actual programming system for a real computer, their IBM 704. It was a LISP implementation written in assembler and LISP with stuff like an interpreter, a compiler, garbage collection, input/output, a kind of read-eval-print-loop, saving memory dumps and loading them, writing/loading assembler code from LISP, and all that stuff which is in a typical LISP implementation since then.
The chapter you linked to even has the title 'The implementation of LISP'.
Check out the LISP 1 manual I linked to sometime.