It's best to go through Mac OS X 10.6. Going directly to 10.7 requires finding and purchasing a Mac OS X 10.7 USB thumbdrive, which costs more than the two separate products.
Mac OS X 10.6 requires an Intel Mac with at least 1GB RAM. Mac OS X 10.7 requires at least 2GB RAM and isn't compatible with PowerPC, Core Solo, or Core Duo Macs.
OS X Lion needs Mac OS X Snow Leopard, so you have to upgrade to Snow Leopard first > http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard Before upgrading, make a backup of your files. To upgrade, insert the DVD and follow the steps of the Snow Leopard installer.
The disc contains Mac OS X 10.6.3, so open > Software Update, to update to Mac OS X 10.6.8, that includes the Mac App Store. Then, to buy OS X Lion, call Apple > http://support.apple.com/kb/HE57 Also, check that your applications are compatible > http://www.roaringapps.com
Instead of upgrading to Lion directly, I suggest you to check that your computer is compatible with OS X Mountain Lion > http://www.apple.com/osx/specs If it's compatible, I recommend you to upgrade to OS X Mountain Lion instead, to get new features. You can purchase it from the App Store