I am not aware of any smart TV that actively solicits a DHCP lease and default route outbound from anything it's plugged into by the 100M ethernet built into a current gen HDMI link. At least not yet. And since I think the default behavior for things like xboxes, playstations and apple TV is not to be a dhcp server and provide routing/NAT, I don't think a lot of things you can plug a TV into (also yet), would provide such function even if the TV tried.

I'm sure somebody at LG is hard at work on fixing this problem.