Plex is Offline or Unreachable on LG TV

That’s a FullHD (1080p) TV (LG).

For LG TVs, Plex officially supports only 4K/UHD sets (Which Smart TV models are supported?).

That version of the Plex client is ~2.5 years old (release notes). It is no longer being updated. Plex has moved to a new version that does not support FHD TVs (preview announcement, release notes).

Even if some kind of work-around exists (I do not know), it would eventually stop working as Plex releases new media server updates.

As @CostaHT mentions, probably time to invest in a FireTV, Roku, etc device.