The debugger of a Lisp system is also not exclusively written in the language (operators, ...) described in the Lisp standard. The standard language is largely independent from a runtime. It says nothing about the implementation technology. The Lisp system could be running on a virtual machine (like many Smalltalk systems), it could be a whole-program compiler to C, ...

For example in LispWorks it's possible to look at a snapshot of a stack in a Debugger, later.