What your experiencing is "delay", which is different from lag, but goes hand-in-hand with it.
Delay is where the game may appear to not be laggy, but move and button inputs are delayed.
The game being sped up or slowed down randomly is lag, not delay. Delay only refers to button inputs. Choppy, slow or fast game play are all part of lag.
You can experience just one of the two, or even both, and it sounds like you were experiencing both.
Welcome to online gaming
All you can do is try with that person again, another time with the right circumstances (noone online on your connection, or theirs for best results).
Or, try and stick to playing people your connection is best with, which is what I do and a lot of other people.
Obviously, you will not always have someone available on your friends list so you will have to venture out into the lobby at times. But basically, you just won't connect perfect with everyone. It sucks, but your at the right place to find other people to play that you connect better with.
