A simple tail-recursive factorial example

factorial.lisp

(defun factorial (number)
  (labels ((factorial-helper (x accumulator)
             (if (zerop x)
                 accumulator
                 (factorial-helper (- x 1) (* accumulator x)))))
    (factorial-helper number 1)))

@cooleynal labels is how you declare local functions in Common Lisp. Remember that Common Lisp is a Lisp-2, so function names and variable names live in different namespaces, using let would create a binding in the variable namespace instead of creating it in the function namespace, which would require me to do (funcall factorial-helper number 1)