They did have reversible washer lids. There were rubber plugs in the hinge holes on what ever side was opposite the hinges. I think this hinging option was only available on certain upper scale machines.
I don't believe this is a Lady Kenmore, I think it is the model down. You can tell by the K emblem along the trim on the front of the machine. If it was a Lady K it would be the bust of a woman instead of the K.
Here's a thread to when Robert found the NIB one years ago:
The "Scoots" button was only available on the Double Delux Lady Kenmores. Not only did it reduced wash time by 30%, but magically also turned laundry into lace.