Hardware test is only on disc 2 "Applications Install Disk", which also contains the bundled iLife apps. You should have been given both discs - it's a licence condition that the discs are part of the computer bundle.
If you have any doubts about the OS install disc, can you check the other identifiers I mentioned earlier - usually under the stand base, and let us know so we can attempt to cross-check.
In order to get Lion, you need OS X 10.6.6 or later to access the Mac App Store and purchase Lion as a download (fast broadband connection needed). Alternatively, it's available on a USB stick from the Apple Online Store for $69 ($29 for the download).
You probably could load Lion directly with the USB stick, but it would be wise to check there's not a RAM issue beforehand, as that could just as easily screw up a Lion install as a Snow Leopard one.
The RAM's not difficult to get at, so shout if you want to try that.