I've been a facing a weird lag when I use my Apple TV as an extended monitor. Till recently, it was fine because I decided to use my Apple TV to watch on the TV (which it was designed for anyway :-))
But, for some reason all my HDMI cables have recently stopped working when I hookup my laptop to my monitor (both an old Macbook Pro 2011 and latest Macbook Air).
This was getting annoying at times when I needed a seperate display. I often used Duet, which is perhaps the best app I've ever bought. It works like pure magic!
Anyways, now I needed a "real" monitor, so I tried to experiment this today.
I plugged in an Ethernet cable into my Mac and then into my Apple TV. I was able to recognize the Apple TV from my Macbook and was able to connect as an extended desktop without absolutely any problem!
The lag seems much lesser and I'm to play Video and Audio with almost no lag!
Awesome! Happy to put my Apple TV 3rd Gen back to some serious work!