So it sounds as though you wiped your drive and it can't find the system (OS startup) folder because there is none (folder with ?).
One more question: did your machine come with Lion?? Or did you purchase it at the app store? If it came with the machine, then it would not show in the app store.
You tried recovery and said it "made an internet recovery" - when you booted up with Command + R, did you at first see a spinning globe? If not, there was no internet recovery. Try restarting with Command + Option + R - on older machines, that is internet recovery (if your machine supports it). You should wind up with a screen like this:
Is this what you saw before? You can erase your drive in Disk Utility. When done, you need to click on Reinstall OS X - it will then go to Apple's servers and download the entire OS. Once downloaded (may take a while unless you have a blazing connection), it will install. It should also recreate a new recovery partition.