I see two problems in your image, but none of them are related to being
unable to redefine lwindow.

The first one is that I omitted a closing ] in the second define-key
command. Sorry. But it seems you corrected it,

The second one is about my-s-d-command, which obviously won't work because
it does not exist. It was just an example command for you to substitute.

So, in other words, if you do

  (setq w32-lwindow-modifier 'super)
  (w32-register-hot-key [s-])

  (define-key global-map [?\s-r] 'list-buffers)
  (define-key global-map [?\s-d] 'make-frame-command)

does lwindow+r run list-buffers? And does lwindow+d make a new frame?