Can I play Minecraft through an external hard drive?

What do you mean on a external hard drive?

I'm not sure what you mean by play on a external drive, but i do know a way that you will lag less.

Press ctr+alt+delete, Then open task manager, go to minecraft, press go to process, and set it to max usage. This will set the priority higher, and help you lag less. Also make sure that you have almost all of your setting low on minecraft, especially render distance.

Yes you can, all you have to do is transfer all the Minecraft files over to the external drive. Or uninstall your current copy and re-install it onto the external drive.

However, unless the drive is significantly faster than what is in your computer it won't make any difference.

Games don't really run from the hard drive, they run from the processor and Random Access Memory (RAM). It's only truly large games that see any impact from hard drive speed. Minecraft really isn't that big, and the drive is not constantly being accessed like is needed for games like Skyrim and the like.

Furthermore an external hard drive is external to the computer, so there are several points of lag between the hard drive and the system. The external drive has to be fast enough to compensate for the speed lost by the indirect connection.

If your internal drive is 5400 and your external drive is a SSD you *might* see some difference. Otherwise I doubt you will see much. You'd probably see more of an improvement by making sure all the background programs on your computer are closed.