Dear John,
I suspect that you are enjoying the use of a wireless connection. Whereas, if you disconnect from the wireless connection (ensure you have the password on hand for re-connection) you may see that you have no internet connection (via Wired Ethernet) whatsoever. If in addition, you unplug the LAN cable (at the SmartTV socket's end) you will note that the repeat message re. Wired Ethernet disappears.
There is an outside chance that your Wired Ethernet connection distribution point (opposite to the end of the LAN cable connected to your Smart TV) may be faulty. To check this, connect some other device e.g. a laptop computer (perhaps even using a replacement Ethernet Cable) and observe whether that device can establish a trouble-free internet connection, or not as the case may be. If you find a trouble free internet connection this way, the problem is narrowed to the LG Smart TV, and it may be either a software or hardware issue, or both of these.