I am adding a new answer to this, as the problem still persists (2023).
The Problem
Adobe Lightroom does not natively support the Sony a7, a9 or a1 cameras. So while Nikon and Canon cameras just work by attaching them and maybe setting the camera up for remote connection, it will not do anything for a Sony.
Solution: Sony Imaging Edge Software
This solution is the cheapest, as you have all the stuff needed for it already at your hands or can get it for free.
- Get Sony Imaging Edge Software from their homepage
- Set up your camera to use PC remote
- Set the Software to save each image to a folder on your computer
- Set up Lightroom to watch this folder and auto import any image in here
- Start up Software, Lightroom and connect your camera
- Start shooting.
Any image should now be saved to your drive, then imported into Lightroom.
Note: This solution is slower than direct tethering support.
Solution: Smart Shooter Software
Tethering Tools offers a software called Smart Shooter (currently version 4, Windows & Mac) which offers a way better shooting experience than the Sony software and includes a Lightroom Plugin for direct tethering.
With that it is simply setting up the camera for remote PC connection, connect and start a tethering shoot in Lightroom.
(This is my preferred way after trying out everything described here.)
Solution: Capture One
Maybe not really a solution: Capture One as an alternative to Lightroom offers native support. The approach of Capture One is quite a bit different. You might or might not like it. It has some strengths over LR in some areas, while lacking in others. Tethered shooting is a strength of it.
Disclaimer: I am neither affiliated with Smart Shooter, nor Capture One.
Newly added support for Tethered Capture in Lightroom 5.3:
in the article. \$\endgroup\$