Elisp disagrees:

  > (lambda () (print "hi"))
  (closure (t) nil (print "hi"))

  > (let ((a 1) (b 2)) (lambda () (print "hi")))
  (closure ((b . 2) (a . 1) t) nil (print "hi"))

  > (let ((a 1)) (defun foo (x) (+ x 1)))
  foo
  > (symbol-function 'foo)
  (closure ((a . 1) t) (x) (+ x 1))

  > (defun bar (x) (+ x 1))
  bar
  > (symbol-function 'bar)
  (closure (t) (x) (+ x 1))

So yes, every function is a closure.