Welcome to the Apple Support Communities
You have to call Apple to purchase Lion > http://support.apple.com/kb/HE57 They will give you a code that you must type into App Store, so the download will start. Make a Time Machine backup and/or a clone with Carbon Copy Cloner before upgrading. Also, see if your apps are compatible > http://www.roaringapps.com
Lion with 2 GB of RAM will run slow, so if you note that your computer is slow, reinstall OS X erasing the disk.
As you have an Intel Core Duo processor, Lion isn't compatible with your computer because Lion requires an Intel Core 2 Duo or later. Lion is a 64-bit operating system, and your processor is 32-bit