Do you have another Mac that you can use to create the installer flash drive?
Here's the sequence to follow:
Purchase Lion
http://store.apple.com/us/product/D6106Z/A/os-x-lion
You get a redemption code that you would use to download the Lion installer from the App Store. You'll need a Mac running at least OS X 10.6.8 to get that download.
Once you have that installer, you can use various methods to build your own installer flash drive.
Get an 8GB size - ideal for the installer.
One method that I use is the app "DiskMakerX" - makes the task very simple, without needing to type in a bunch of terminal commands.
http://diskmakerx.com/whats-this/
Get the older version 3.0.4 - which works best with Lion.
When you finish making that flash drive, you can boot to that drive, (you know how to choose a startup drive from the Option-boot menu
) which will give you a menu screen with several choices - where you can choose Disk Utility.
Click on the device line for the SSD (which shows SSD model number, etc), then the Partition tab.
Choose 1 Partition from the Partition Layout dropdown. Name the new partition, if you like (otherwise it will be named a default (Untitled 1 or whatever)
Double check that the Options button shows GUID partition table, and click OK.
Check that the Format will be Mac OS Extended (Journaled), then click the Apply button.
The process only takes about 30 seconds. When it completes, you can Quit Disk Utility, and continue on with the OS X Reinstall. It will take 30 minutes to an hour. (might be slow on your vintage MBAir, so be patient)
And, there's a new user setup before you can use your MBAir, but that should all be successful.
Come back if you need more help - or get totally stuck...
