(let ((key (kbd "S-<down>"))
      (def (lambda ()
             (interactive)
             (unless (evil-visual-state-p)
               (evil-visual-state))
             (evil-next-line))))
  (dolist (map '(evil-normal-state-map evil-insert-state-map))
    (define-key map key def)))

Wrong type argument: keymapp, evil-normal-state-map