Why doesn't light room support tethered capture on sony?

John is right. I am pretty sure Adobe only provides tethering support for cameras where the manufacturers supply a working SDK for tethering. Canon, Nikon, phase one and I believe Leica do so they are supported for tethering. Sony doesn't. Not much you can do but ask Sony to provide a tethering SDK.

Many over the years have asked Adobe in their official feedback forum why they don't support tethering of Sony cameras. There have been a few incomplete answers.  Sony never provided a publicly available SDK (software development kit) for tethering over a cable. They did provide an SDK for wireless tethering, but an employee hinted that the engineers didn't find it suitable (no reasons given); but regardless, Sony has withdrawn support for that SDK.  PhaseOne provides wired tethering of many Sony cameras as part of their closer business partnership with Sony, presumably using a privately available SDK or in-house engineered tethering based on specs provided by Sony.  Adobe has never commented on why they haven't wanted to or been able to partner with Sony (that's not the sort of thing they every comment on).

You can add your feedback on this issue to this topic in the official feedback forum: Lightroom: When will my camera be supported for Tethering? | Photoshop Family Customer Community . Adobe product developers read everything posted in that forum and infrequently reply.

We're not Adobe here in this forum, we are just other users, we can't answer "why" Adobe does or does not do something. Even the occasional Adobe staff person who replies here only provides technical support, I have never seen them answer "why" questions.