Okay, it's coming on the end of my shift and I don't want to leave you hanging.
However, based on the information you supplied, I think you need to do the following;
Please go up to the "Utilities" menu at the very top of the screen and choose Terminal.
diskutil CoreStorage list
and press enter
You should get a screen similar to this:
Note the long string in the red box that is next to Logical Volume Group with the name Macintosh HD. This is called the UUID.
diskutil CoreStorage delete UUID
(where "UUID" is replaced with the string you identified)
and press enter/return.
Once the CoreStorage volume has been deleted, you should be able to return to Disk Utility and format the hard drive. You may or may not have to restart the system and return to the Recovery HD partition first (Command-R at startup).
In Disk Utility, select your normal, physical hard drive from the list in the sidebar and then choose the "Partition" tab.
Under Volume Scheme, click "Current" and choose "1 Partition".
Name your hard drive on the right side (usually "Macintosh HD") and choose "Mac OS Extended (Journaled)" as the format.
Click options and verify GUID partition table is selected and click OK.
Now click Apply.
Once the process has completed, exit Disk Utility.
In order to reinstall OS X Lion or OS X Mountain Lion, you will need to be connected to an Ethernet or Wi-Fi network. The Wi-Fi menu item is in the upper-right corner of the screen. Click the icon to display all available Wi-Fi networks. Click your preferred network name and, if needed, enter a username and/or password.
Then on the Mac OS X Utilities screen, choose to Re-Install OS X.
It should lead you along after that and complete the installation.
If you run into additional issues, reply back and I will try to check my email for the next hour or so.
After that I will return tomorrow (Thursday) around noon ET (GMT-5).