One thing is to have lag and another to have low FPS, given your specs I'd say it's a lag issue, however you might want to measure your fps, just in case.
Now about the lag, you may have a great connection and still have lag issues. Lag spikes may arise if there's another program taking over the connection. A download would take most of the bandwidth and interfere with the game.
Note that this download might or might not have been started by you. There might be another person on the network downloading something or a program might be updating itself.
You can use programs such as Net Limiter to monitor your network traffic an find possible leaks.