Cannot Unmount Mac OS X Base System Disk
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.
I think you need to reset your PRAM (for older Mac computers) or NVRAM (for newer Mac computers):
http://support.apple.com/kb/HT1379
Resetting PRAM or NVRAM
- Shut down the computer.
- Locate the following keys on the keyboard: Command(⌘), Option, P, and R. You will need to hold these keys down simultaneously in step 4.
- Turn on the computer.
- Press and hold the Command-Option-P-R keys. You must press this key combination before the gray screen appears.
- Hold the keys down until the computer restarts and you hear the startup sound for the second time.
- Release the keys.
This should get rid of the "Mac OS X Base System" virtual mount, and allow you to clean install from your Lion USB drive