The Lisp community was at the forefront of research into object-oriented programming; ANSI Common Lisp has very nice object system for doing "objects with state". Cons cells have been mutable in Lisp going back to the beginnings. Mutable arrays are described in a 1960 reference manual.

Imperative programs can easily be written in Lisp or translated to Lisp from other languages.

Common Lisp even has a form of "go to".

I'm afraid the disconnect is between what you know and what you're talking about.