I've got this exact same issue on my LW650T and have posted about it in another thread. I found one other reference to it on another forum, and that person had Macs on his network - as do I.
My Tv is connected via Ethernet and there are a few Macs on my network, including an always-on Mac Mini which I use both as a general server and as my HTPC. Restarting any of the Macs causes the Pairing Key to pop up and occasionally bringing an iPhone or iPad (connected on the network) out of sleep will also cause it to pop up. Other times it just seems to pop up of its own accord! The Mac Mini has all sorts of server processes running (OS is Lion Server), but I've not been able to isolate any particular service - for example it seems starting and stopping the DNS server process will consistently cause the key to pop up, but even with that disabled completely and using an external DNS instead I'm still getting the Pairing Key popup seemingly at random and when restarting other Macs on the network. I've been driving myself mad trying to fix this and the only solution I've found is to take the TV off the network, which is not much of a fix when I use the online features a lot. I also use both DLNA and Plex on the LAN.
I did call LG Support for a chat and they said that hadn't encountered the issue before. They seemed to take it quite seriously and put me on hold while they consulted with a couple of different folk there, but couldn't come to any resolution.
Any tips on how you configured your firewall, as my attempts to do the same haven't solved the problem...