How to download purchased Lion?

What OS are you presently using?

If your computer is capable of running Mavericks, then that's what you will have to do. The App Store will not let you download Lion if you can run Mavericks.

If you bought Lion from the Apple Store online then you should receive two emails, however it takes about three business days. One email will have a locked PDF. The PDF contains the redemption code to use in the Mac App Store. The second email has the password to unlock the PDF.

No cost for Mavericks. It's a free download. I'm afraid that in order to download Lion on your other computer you will have to reinstall Snow Leopard on it. Then the App Store will allow you to re-download Lion. If by chance you decide to go that route, then I suggest that you save the Lion installer for future use before installing it. Better yet you can use the saved installer to make a bootable USB flash drive installer.

I wish I had a better solution for you. I doubt you want to spend another $20 for the download. Besides, the App Store won't let you download it on the computer that can run Mavericks, and it won't let you download it on the computer that already has Lion installed on it. Sort of a Catch-22.

Yes, I know. I hope you took my suggestion to save the installer application so you can make a USB flash installer. If you did, here's how:

Make Your Own Mavericks, Mountain/Lion Installer

After downloading the installer you must first save the Install Mac OS X application. After the installer downloads DO NOT click on the Install button. Go to your Applications folder and make a copy of the installer. Move the copy into your Downloads folder. Now you can click on the Install button. You must do this because the installer deletes itself automatically when it finishes installing.

2. Get a USB flash drive that is at least 8 GBs. Prep this flash drive as follows:

1. Open Disk Utility in your Utilities folder.
2. After DU loads select your flash drive (this is the entry with the mfgr.'s ID and size) from the leftside list. Under the Volume Scheme heading set the number of partitions from the drop down menu to one. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, set the partition scheme to GUID then click on the OK button. Click on the Partition button and wait until the process has completed.
3. Select the volume you just created (this is the sub-entry under the drive entry) from the left side list.
4. Click on the Erase tab in the DU main window.
5. Set the format type to Mac OS Extended (Journaled.) Click on the Options button, check the button for Zero Data and click on OK to return to the Erase window.
6. Click on the Erase button. The format process can take up to an hour depending upon the flash drive size.

3. Use DiskMaker X to put your installer clone onto the USB flash drive.