Lightroom tethering relies on the provision, by camera manufacturers, of a Software Development Kit ( SDK) from which Adobe can extract the necessary code to enable tethering.
Canon, Nikon and Leica provide an SDK. Other companies - like Pentax and Sony - don't, which is why there's no tethering support in Lr for their cameras.
But Olympus does provide an SDK, which I understand includes the necessary code for tethering, so maybe Adobe needs a nudge:
I sent the same request to Olympus. I had to log in on their FAQ page as a owner of a newer camera, but once I got to the free form comment section, I was able to present my request. A few days latter I was given a link to access Olympus's studio software and a password code to set it up. I have not had time to check it out completly, yet