Well, I remember the video having exact counter-play.
A kill lane was classified as someone putting damage onto the opponent over cs'ing (under turret).
A farming lane was a last hitting lane but played defensively.
A pushing lane was a farming lane but with a more agressive-style less focused on hitting your opponent.
A roaming lane is obviously those champions that are great at roaming and ganking other lanes.
So
When your opponent is trying to kill you, I think to counter-play you play for farm.
When you are against a farming lane, obviously you want to push him under turret.
Against a pushing opponent, I think you want to be the kill lane so you can keep him from pushing minions into you.
Against a roam, obviously you would love to be the pushing mid-laner.
If you don't agree with me? Play ball