Cannot Unmount Mac OS X Base System Disk My Mac running Lion was being slow, so I was decided to reinstall OS X. I don't have any Time Machine backups.

Everything went file, but in the middle of the installation, it got stuck, and later the installation failed without any reason. So, I tried to reboot again, but it said that the reinstallation failed and asked me to reinstall again. I tried to reinstall, but nothing came up.

So I tried to use Disk Utility to erase the startup disk and make a new partition. But, when trying to partition, Disk Utility said that it cannot unmount the disk. In Disk Utility, I found another disk called disk2 and Mac OS X Base System. As far as I know,  I didn't see that disk2 in my disk list before.
I tried to unmount it or erase that disk2, but it won't let me. So I tried using Terminal to force unmount that disk, but still it doesn't let me.

Is that disk2 the reason why I cannot partition my main HD? How can I unmount or erase that disk2 Mac OS X Base system ? 

I would like to clean install OS X lion again. I already have a boot image on my USB drive. I just cannot start it because the installation fails and something is still running, I guess.

Screenshot of Disk Utility:
The Mac OS X base system image is not the cause of your problem. See What is the 'Mac OS X Base System' disk image on my 2011 MacBook AIr? for an explanation.

My best guess, based on the screenshot, as to why you can't repartition the Hitachi disk is that it's the current startup device. You need to restart your computer from an an external device—preferably a device that has the Lion Installer on it-if you want to reformat the drive. Otherwise, assuming you have a valid recovery partition, you can erase the Mac partition itself and reinstall Lion without an external device.

Perhaps Apple's Mac OS X 10.7 Help: Recover your entire system document will help you.