I was paying for a really fast connection until recently, and still had lag, so Im prone to think its their servers.
Is it a new feature? I thougt the single player bit had been going for a while?
Could be opponent's connection?
I used to play a lot on a pretty decent connection (60/60 Mbit), and usually there was no lag, but sometimes there was and every once in a while it was so bad it wasn't even possible to properly play the game. Noticed it was always consistent throughout the game whenever it happened though, so figured it was most likely because if my opponent's connection.
When you're at the "choosing home/away kit" screen there's a 3 bar thingy sort of blinking either green, yellow or red (or switching between either) and showing 0-3 "bars". If that often spikes down to 1 or 0 bars and/or the colour red I think that means your opponent probably has a slow or unstable connection.