I can plug the DSLR right into the computer and tether it into lightroom. Is there an adaptor or anything that will allow the OSMO to do the same?

I,ve never tried it but there is a micro usb port for downloading of the sd card, I don't think you can tether, but plug it in and see if it works.

Seems like the wrong tool for the job.  You don't tether a DSLR if you are going to be running around outside (or even inside).  Tethering does not seem like much of an issue, since this would be a terrible camera for tethering.

OSMO would be a great camera to tether.  I disagree with Mabou2. There's no need for a tethered studio camera that lives on a tripod to have a screen, a viewfinder and a bunch of physical controls.  I don't get why no one has made an M43 tether-only body.  OSMO would be the closest thing to that -- if it could tether.