There is lag?
I've played a few 360 games this way, and the lag is not noticable mostly. The only way I noticed lag was cod ghost, turning the stick sensitivity to max and did a bunch of hurky jerky spins and snap aims and there was a slight lag. most things are very playable. I wouldn't play cod games online though as millerseconds from connection, tv response, and controller to console already decides who wins a one on one shoot out as it is, not point adding another factor to that.
http://imageshack.com/a/img801/6426/f7pc.gif
^Yes that's me ripping it up in the GIF. :)