I’ve had no issues running Live TV - either Plex Channels or Live TV & DVR channels - on iPhone iOS or any other client. But, I’m not running any virtualization or containers. Just a dedicated Ubuntu server running Plex.
You might want to read through this post:
https://forums.plex.tv/t/client-says-it-wont-play-from-remote-server-although-the-server-is-local/921148
In particular, you might want to make sure that your iPhone can connect to the plex.tv servers and that your DNS is working properly.
Adding your LAN netmask to the list of IP addresses that can connect without authorization may help also.
One additional item to check: The iOS apps should be working okay for Live TV as long as you have Plex Live TV enabled in the settings. Settings → Online Media Sources → General - Live TV → Enabled.
Plex says that this will be fixed in the next release so that you will be able to disable Plex Live TV.