Reinstall OS X Lion on Macbook Air 2012

You could make a bootable drive with the Lion installer. To do so, you'll need the original Lion Installer, downloadable from the Mac App Store once you've purchased it and a USB flash drive with a GUID Partition Table format. You'll find here a step by step guide for the formatting part. Afterwards just:

1. Go to the Applications folder and find the installer, which should be called Install Mac OSX Lion.app.
2. Right+click on it and choose Show Package Content from the contextual menu.
3. Under Contents / Shared Support you'll find a file called InstallESD.dmg, drag it to Disk Utilities' sidebar and mount it.
4. Select the installer and click the Restore button.
5. The installer should appear in the Source field, if not, drag it there.
6. Connect the USB and drag it into the Destination field.
7. Click Restore.

If everything was done correctly, you'll, then, have a drive from which you'll be able to boot just by holding C while restarting your computer.