It is hard to believe that a game as light weight as MineCraft (especially graphics wise) would lag on a 270X.
Try using an OSD like Riva Tuner Statistics that comes with MSI Afterburner. Try monitoring CPU usage, GPU usage, GPU temperatre, and framerate.
When you experience the "lag", first look at your framerate, has it dropped? If not, the graphics card isn't the cause of the "lag". Next look at your CPU usage, is it quite high. If so, then your CPU is bottlenecking you or there is a problem such as throttling or a background application causing the problem.
If your CPU usage isn't the culprit, look at the GPU usage and temperature. Is the GPU usage high? If so look at the temperature, is it hot? If it's hot, then it could be that your GPU is throttling. If it isn't then your GPU is actually the bottleneck.
If after all this none of this seems to be the problem, it's probably your internet connection, which is what I'm leaning towards.