After thinking about it, I determined that it couldn't have been Yeoman or any of my Ubuntu server's fault, because nothing changed after I wiped the machine clean and started over. It wasn't a blocked IP on the browser either, because both Chrome and Firefox had the same problem. It wasn't a blocked IP on my client machine because the problem persisted on another machine.
The light bulb went off when I actually looked into the exact URL livereload was requesting. It was requesting on port 35729, a port I haven't opened up on my AWS EC2 account!
After I opened up that port, it worked flawlessly!