If you're streaming via AppleTV, why do you need to give the TV itself access to the network?
I could possibly do it via HDMI CEC, but I have a couple of Sony Bravia TVs that more often than not completely ignores that, so I prefer having control over assuming it happens.
I believe LG doesn’t advertise such an api via Bluetooth
One could build a IR emitter but you need soldering skills for that or buy a usb one which cost north of 30€ + shipping.