(progn
  (while-let ((run t))
    (message "Running")
    (setf run nil))
  (message "out of loop"))

It ends in infinite recursion. setf/setq have no effect on the lexical variable.

I tooka look, but I don't understand why is it necessary to build while-let  on
if-let. This simplified version did it for me:

(defmacro while-let (spec &rest body)
  "Bind variables according to SPEC and conditionally evaluate BODY.
Evaluate each binding in turn, stopping if a binding value is nil.
If all bindings are non-nil, eval BODY and repeat.

The variable list SPEC is the same as in `if-let*'."
  (declare (indent 1) (debug if-let))
  (let* ((bindings (if (and (consp spec) (symbolp (car spec)))
                           (list spec)
                         spec))
         (variables (mapcar #'car bindings)))
    `(let* ,bindings
       (while (and ,@variables)
         ,@body))))

(progn
  (while-let ((run t))
    (message "Running")
    (setf run nil))
  (message "out of loop"))  => "out of loop"

Or did I missunderstood how to use while-let in subr.el?