That's not quite true. You would not see Lisp code written as though it were assembly, full of gotos and working with a finite number of registers, to take an extreme example. Lisp is a multiparadigm language, but it is heavily functional. As such, writing imperative code is not generally advisable ("not in the spirit of Lisp"), but is possible. Similarly, code with such a heavy use of variables is likely unfunctional, and thus would similarly be outside the "spirit of Lisp". Yes, you can do anything you want in Lisp (cf. the Church-Turing thesis), but it may not be advisable ("in the spirit of Lisp"). Again, for instance, if you want to work in a stack-based manner, it would probably be advisable to either (1) rework your code, or (2) switch to a stack-based language like Factor.
This is not unique to Lisp: if you want to write a tail-recursive, functional, list-based program in C, that's probably not a good idea. You can, but since C is optimized for iteration (with many implementations not even supporting tail call elimination) and for imperative programming (it lacks closures and anonymous functions), and since memory management in C is…clunky…you would be better off (1) reworking your code, or (2) switching to a more functional language with lists and tail call elimination, such as a Lisp.
In short, yes, as a Turing-complete language, Lisp can do anything. And as a multi-paradigm language (with macros), it can do a good job at performing a given task in any way. But it has strengths, inclinations, and intentions, which together do comprise what could be called a "spirit of Lisp".
