There is actually a very easy way to playback Dolby Vision (DV) video shot on the new iPhone 12 lineup to the LG TVs (e.g. C9 OLED) that support DV.
Just download the LG TV Plus app from the App Store -
https://apps.apple.com/in/app/lg-tv-plus/id838611484
Connect to your TV (both phone and TV must be on same WiFi network - preferably 5 Ghz with a strong strength).
Then simply playback the DV video from within the app to the TV. It'll play in the DV mode, and you'll see the familiar DV logo pop in from the top right when the video starts playing.
In my experience, this is the best pay to playback video shot on the iPhone to the LG TV. The recent TVs may support Airplay 2, but even with a high end router the quality is poor, and there is plenty of stutter. Whereas from this app, everything plays without a hitch and in great quality, as if the file was being played locally via a USB stick.
Tested on an iPhone 12 Pro Max and a 65" LG C9 OLED.