Q: Brand new lion and mac air, corrupted!

No, you shouldn't get that message. Something sounds very wrong there. You're only downloading the installer, not the app.

You could try searching to see if the installer still exists in your Applications folder (Look in Applications > LionInstaller.app) in which case you don't need to do any of this. Just click on it and follow the directions.

Failing that, go with your brother's download, though I'm not sure how you're going to get a 4GB file sent to you...

To install on a USB follow the advice from the link Thomas posted above:

Installing Lion on an external storage device

Use these steps to install Lion from your Mac to a different internal hard drive or to an external USB, Firewire, SDHC or SDXC card, or a Thunderbolt storage device.

Important: This will erase the storage device. A storage device that is already formatted to support Windows (formatted for FAT or NTFS file systems) will be reformatted. You should back up any important files that are on the device to a different drive.

1. Attach a USB, FireWire, or Thunderbolt storage device to your computer, or insert an SDHC or SDXC card into the SD card slot if your Mac has one.
2. Launch Disk Utility, from the /Applications/Utilities folder, then click Continue.

Erase and reformat the storage device

1. Click the attached storage device where it indicates it's size in GB.
2. Click the Partition tab.
3. Select "1 Partition" from the Partition Layout pop-up menu.
4. Click Options. Note: Do not select more than one partition.

5. Click the GUID Partition Table radio button, then click OK.

6. In the format field, select Mac OS Extended (Journaled).
   
7. Click Apply.
8. Enter a name for the drive in the Name field.
9. Verify that you wish to erase and reformat the selected drive by clicking Partiton.
10. After the reformatting process is finished, choose Quit Disk Utility from the Disk Utility menu.

Install OS X LionIf you completed your installation of OS X Lion, your installer may have been removed after your successful first login to OS X Lion. Mac App Store's Purchases page should show Install Mac OS X Lion as being "Installed", and disallow its download, when viewed from a computer running OS X Lion.To redownload the installer on a computer running OS X Lion, press and hold the Option key while you click the Purchases tab. If the button to the right of the Install Mac OS X Lion item doesn't change to "Install" and allow you to download Lion, use Spotlight to search for "Install Mac OS X Lion" on your computer.

1. Launch the Install Mac OS X Lion installer you downloaded from Mac App Store. The installer should be in the /Applications folder.
2. Follow the on-screen instructions to complete the Lion installation. Be sure you install Lion on the external storage device you've connected for this purpose, not your computer's boot drive.
3. When installation to your external device is complete, you can re-run Install Mac OS X Lion installer and upgrade the boot drive of your computer. A Recovery HD will likely not be created, but if you need to reinstall or repair your boot drive at a later date, you can connect the external drive you just prepared and hold cmd-r while restarting computer in order to boot from the external Recovery HD.

Please note that Recovery HD must be present on your computer's startup volume to use FileVault 2 (not an external Recovery HD).

 

It's not often you get people on the Internet willing to help some stranger so much...

Well, fortunately for us all (we've all made use of it at some time), that's the way community support forums work!

 

I really appreciate you taking your time to help me.

No problem, you're welcome! 

To be honest, if you live anywhere near an Apple store (I don't know - did you buy the MBA in a store  or online?), that's exactly what I'd do: take it into the shop and get them to sort it out. You don't need to go through all this hassle yourself unless its inconvenient to get to the store. Your machine is under warranty and if there's no Recovery HD on there then it was obviously not set up correctly in the first place.

I wonder what is going on, this is so confusing lol, when I try to install it that way it says " this version of mac osx 10.7 cannot be installed on this computer"

I suspect that this is, as Thomas pointed out, because your machine came pre-installed with Lion. In any case, I'd take it to the shop if I were you, as I said above.

EDIT: Oh sorry, just saw your post above. Yeah, you might be best off trying to sort it out yourself first, then. In any case, you'll learn a bit about Mac OS in the process...

Sorry, I just realised the instructions I gave you before were not for making a USB boot drive, but for installing Lion on an external disk. To make the bootable USB drive, follow these instructions (these are the ones I used so I can vouch it works!):

http://www.redmondpie.com/how-to-make-your-own-os-x-lion-bootable-usb-flash-driv e-tutorial/