You have acted on faulty information. I have to guess that if you don't have the App Store app on your Mac (Apple menu), then you have OS X 10.5 Leopard or earlier. Which means that your Mac may be limited in how far you may upgrade the OS. That said, the first version of OS X that you would need to buy is OS X Snow Leopard 10.6. It is available from the Apple telestore where you bought OS X 10.7 Lion. However, Snow Leo comes on a DVD that will be sent to you in the mail.
Once you have installed Snow Leo from the DVD you need to download and install the 10.6.8 update combo in order to have the final release of the Mac App Store installed on your Mac.
OS X Snow Leopard 10.6.8 v1.1 update combo
http://support.apple.com/kb/DL1399
Then you may use the redemption code to download the Lion installer. However, if you have set your sights on a newer version of OS X, and your Mac can support it, Lion would be a waste of time. OS X 10.8 Mt Lion is also a paid upgrade and can be installed over Snow Leo. But almost any Mac that can run Mt Lion, can also run OS X Mavericks 10.9 and that is a free upgrade from Snow Leo.
System requirements for OS X Lion
http://support.apple.com/kb/ht4949
System requirements for OS X Mountain Lion
http://support.apple.com/kb/HT5444
System requirements for OS X Mavericks
http://support.apple.com/kb/ht5842