You’ll also pick up TrueHD + Atmos and dts/-HD/:X passthrough with the Shield.
Connect the Shield directly to the Sony. LG blocks dts passthrough for devices attached to HDMI inputs on the TV. See Audio Passthrough section of LG C1 review at rtings.com.
The Shield is not without its own issues. Blu-ray rips from discs with seamless branching may have problems with audio sync and dropout at the branch point. It usually appears on extended cuts of movies. The workaround is to stop / restart playback once past the branch point.