Pharo / Squeak smalltalk.
As such basically ALL software of the MIT Lisp Machine is heavily object-oriented - unlike GNU Emacs. It uses an extensive graphical/textual GUI layer and abstractions like applications, command loops, servers, clients, ... On the Lisp Machine an editor is an application, but not the main abstraction (unlike GNU Emacs) - even the Listener on Lisp Machine is not in any way related to Emacs (minus some keyboard commands).
Thus the closest software stack to the Lisp Machine are by far Common Lisp + McCLIM + McCLIM-applications (like the McCLIM listener and others) and Common Lisp + CLIM + CLIM-environment.