That's slightly backwards.
The second Emacs (after TECO) was written in Lisp. On a Lisp Machine. Stallman later went for an Emacs, GNU Emacs, written on top of Lisp VM implemented in C. That one then got support for 'inferior' Lisps, external Lisp processes run from GNU Emacs. Extensive modes were ILISP and ELI. Slime is kind of a reimplementation of ILISP.
Clozure CL goes back to Coral Lisp, an early Lisp for the Macintosh, written in the mid 80s. Coral Lisp, and the Coral Common Lisp, and then Macintosh Allegro Common Lisp and then Macintosh Common Lisp all were written mostly in Lisp and had an Emacs-like editor (FRED - FRED Resembles Emacs Deliberately) included plus a bunch of tools: backtrace, inspector, interface designer, Editor-based Listener with REPL, etc. The main difference to GNU Emacs: it was focused on Common Lisp programming, it was implemented all in Common Lisp, it all ran in one application (no external Lisp), much of the tools made use of the GUI toolkit from the mac (menus, dialogs, buttons, copy/paste, AppleEvents, ...).
MCL then was dead end, because it was tied to the old Macintosh libraries.
OpenMCL was a fork initially thought to run on the spaceship mentioned before (but it was actually LispWorks, which was used for the spaceship). It was stripped down and ported to Unix or something similar. OpenMCL, later renamed to Clozure CL, was brought to the new Mac OS and got a simple IDE, but not based on the MCL code, but using some of its IDEs.
So Clozure CL's IDE goes back to the old MCL IDE and to Hemlock (the Emacs-like editor from Spice Lisp / CMUCL). It's not based on remote/external execution, like Slime.
Clozure CL's IDE is very simple, offers not many tools, and those tools are not really powerful. For MCL there were much better IDE tools developed. But MCL is gone.