Create an exemption from the demand to be signed in to a plex account. This is done by putting the particular device's local IP address into the Plex server configuration.
(This is possible from Plex Server version 1.1.3 onwards)
Settings - Server - Network - SHOW ADVANCED - 'List of IP addresses and networks that are allowed without auth'
: it appears that for LG Medialink clients one has to insert the whole local subnet and not just the LG's single IP address e.g. 192.168.2.0/24
[edit 2]: further investigation conducted by @sa2000 suggests that entering the TV IP and the Server IP and if more than network card active on the server then all the server IPs need to be listed. So no need to whitelist whole subnet.
you need to determine the IP address of the particluar plex client for which the exemption shall be made (the user interface of your router should tell you [or the network configuration in your tv])
you need to make sure that the device keeps on using this same IP address, even after a firmware update or reboot of your router or extended powered-down periods (either by assigning the device a fixed IP address or by using DHCP address reservation [in your router configuration])
- more effort needed