Common Lisp is a multi-paradigm language. The standard supports imperative, functional and object-oriented programming styles. It even tries to mix them. The Common Lisp Object System for example uses Generic Functions, and not the more usual message passing mechanism. The language is also traditionally extended by other paradigms: rule-based, logical, actors, agents, concurrent, ...
Still Common Lisp uses mechanisms of functional programming widely. It supports lexical binding, many library functions are higher-order functions, etc. There are also some programs which are written in a very functional style and most implementations support tail call optimizations to further make a functional style useful.
Common Lisp does not enforce a particular programming paradigm. As a start all three supported would be used by a programmer. He or she might even add some more, if necessary.
Lexical binding, higher-order functions, etc are very common in Python, for example. Except for TCO which is not widely supported in Python, and problematic if support is not guaranteed, Python seems to be just as functional as CL. Nobody cites Python as a functional language, yet people mostly cite CL as a functional language.
Some Common Lisp code I saw was also very imperative.
Scheme seems to be a more functional language, but I don't really see why people consider other Lisps any more functional than say, Python.