I assume that this TV doesn’t have a real Plex client, but just a generic DLNA player.
With DLNA clients, you can only play the file as-is. If the TV doesn’t have an AC-3 decoder, then you’ll have no sound. Transcoding will only work with DLNA if there is a fitting hardware profile, which describes in detail which file formats and which codecs this device supports.
Developing such a profile is very challenging and the results still won’t work as well as a real Plex client.
Therefore your best bet is to get a FireTV or a nVidia Shield and plug it into the TV.
