No, I was completely disconnected from the internet when the lag started. The game performs normally when I'm connected to the internet through Origin. It's when I'm offline in Origin that the lag happens. That's what's so confusing about it all. If I start up the game while Origin is connected to the internet, I can turn off the internet on my laptop (not touching the settings on Origin at all) and the game still thinks I'm online and plays just fine. But if I start it with Origin in Offline Mode or while completely disconnected from the internet, then the game is laggy and unplayable.
I'm starting to wonder if maybe there's a problem with my Origin files even though I updated it right before I bought and downloaded the game.