"this apple ID was not used to purchase OSX Lion"

Lion didn't come on a disk - it was the first of the download only versions of OS X. If it's a late 2009 iMac it would have come with OS X 10.6.x Snow Leopard. There should be two grey disks that came with the Mac: Disk 1 for the OS and Disk 2 for the iLife apps.

My guess is that you'll need to install 10.6.x from the disk, once installed do software update to bring it up to 10.6.8, go to the App Store in the Apple Menu, login with the ID that purchased Lion and go to the purchases tab to see if Lion is available to re-download.

You could, of course, install Snow Leopard and then upgrade to Mavericks for free, so long as you are happy to do that and check that any third-party apps you rely on will work in Mavericks.

Perchance, was there a USB Thumbdrive version Lion 10.7 included with the computer

when it was new? If you had that, (as the computer likely shipped with 10.7 installed only

if it had a backup installer) then you could install from there.

If the computer has an internal optical drive, there should have been grey-label install

restore media discs (DVD specific to that model build) with applications & OS X on it.

Such an original DVD disc set would also have an Apple Hardware Test on DVD.

The 10.7 Thumbdrive version was offered on a limited basis, no longer available, at $69.

Per the MacTracker database, the only model shown which shipped with 10.7 installed

and also had an optical superdrive, was the iMac (21.5, Late 2011) model. Earlier model

versions show the shipped OS X on media (DVD) as being OS X 10.6.x Snow Leopard.

Avoid Mavericks if you have/possess older software that you would be using regularly.

There may also be a firmware update that could make it hard to revert to the original

OS X version if the Mavericks is installed on certain models that supported it later.

Good luck & happy computing! 🙂

You're welcome.