Lightroom cannot show that metadata field. You can see it in preview.app (if you have a mac, it's in get info in the camera specific tab), in Photoshop, or in exiftool and many other utilities.
And why not to do it in LR?
If you have Photoshop, the file properties show shutter actuations.
Opanda IEXIF Viewer is a free utility for Windows that shows actuatoins:
Irfanviewer also works.
Google "shutter actuations" for other solutions.