I may be presuming too much, but it sounds like you're not aware that the Mac App Store is an entirely different thing to the various wares sold inside iTunes.
The Mac App Store is available on your machine IF you are already running Mac OS X 10.6.6 or higher, so first thing to do if you're not is upgrade to that level. Once that's done, the Mac App Store will be on your Dock (on the far left).
Launch the Mac App Store, sign in (using your iTunes account information), and if for some strange reason Lion is not all over the front page, type it into the search bar. Then buy it exactly as you would any other app.
I'd strongly recommend both a complete backup of your existing system as-is (both Time Machine *and* a bootable clone to a different drive) and a going over with your utility tool of choice to make sure permissions, caches, fonts and other ephemera are ship-shape. THEN do the upgrade.