There is a bit to much simplification here, and confusing terminology going on here. Lisp Machines did not have "processes" (as in, Unix processes); a Lisp Machine process just a function - with some special properties.

The Lisp Machine only had one processor for the Lisp Machine, and it did absolutely support multi-processing and multi-threading.

A good explanation can be found in the Lisp Machine manual:

  https://tumbleweed.nu/r/lm-3/uv/chinual.html#Processes
  https://tumbleweed.nu/r/lm-3/uv/chinual.html#Stack-Groups

Which is also where all current work on the MIT Lisp Machine is being done. :-)