The fact that you have 120 MB broadband is irrelevant.
And no one promised no lag on the Xbox One. There is always lag. Until we get a faster internet that is faster than light then there will always be lag.
Now if you are comparing the two camera positions on your TV being off that happens in a lot of offline and online games. Its nt even lag. The developers purposely delayed each player. For example I got an image from gears where it is off by more than half a player. And they arent even moving.