Do you still have a Recovery HD partition on your computer's drive? If you do, then you should be able to do the following:
Open the App Store and sign in with your Apple ID used to purchase Lion. Click on the Purchases icon and see if your Lion purchase is not listed. If you don't see it, then it may be invisible: Mac App Store- Hiding and unhiding purchases. If this doesn't work, then try:
Install or Reinstall Lion/Mountain Lion from Scratch
Be sure you backup your files to an external drive or second internal drive because the following procedure will remove everything from the hard drive.
Boot to the Recovery HD:
Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Erase the hard drive:
1. Select Disk Utility from the main menu and click on the Continue button.
2. After DU loads select your startup volume (usually Macintosh HD) from the
left side list. Click on the Erase tab in the DU main window.
3. Set the format type to Mac OS Extended (Journaled.) Optionally, click on
the Security button and set the Zero Data option to one-pass. Click on
the Erase button and wait until the process has completed.
4. Quit DU and return to the main menu.
Reinstall Lion/Mountain Lion: Select Reinstall Lion/Mountain Lion and click on the Install button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible
because it is three times faster than wireless.
And, if you still have no success: You can purchase Lion by contacting Customer Service: Contacting Apple for support and service - this includes international calling numbers. The cost is $19.99 (as it was before) plus tax. It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.